Recent zbMATH articles in MSC 81https://zbmath.org/atom/cc/812023-09-22T14:21:46.120933ZUnknown authorWerkzeugCombinatorial necessary conditions for regular graphs to induce periodic quantum walkshttps://zbmath.org/1517.051032023-09-22T14:21:46.120933Z"Kubota, Sho"https://zbmath.org/authors/?q=ai:kubota.shoSummary: We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular mixed graphs to be periodic. One useful necessary condition is that if a \(k\)-regular mixed graph with \(n\) vertices is periodic, then \(2n/k\) must be an integer. As an application of this work, we determine periodicity of mixed complete graphs and mixed graphs with a prime number of vertices. Furthermore, we study periodicity of mixed strongly regular graphs and several classes of mixed distance-regular graphs, and extend existing results to mixed graphs.Strict positivity and \(D\)-majorizationhttps://zbmath.org/1517.150132023-09-22T14:21:46.120933Z"vom Ende, Frederik"https://zbmath.org/authors/?q=ai:vom-ende.frederikSummary: Motivated by quantum thermodynamics, we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action on any full-rank state, and that the image of non-strictly positive maps lives inside a lower-dimensional subalgebra. This implies that the distance of such maps to the identity channel is lower bounded by one. The notion of strict positivity comes in handy when generalizing the majorization ordering on real vectors with respect to a positive vector \(d\) to majorization on square matrices with respect to a positive definite matrix \(D\). For the two-dimensional case, we give a characterization of this ordering via finitely many trace norm inequalities and, moreover, investigate some of its order properties. In particular it admits a unique minimal and a maximal element. The latter is unique as well if and only if minimal eigenvalue of \(D\) has multiplicity one.Z-eigenvalue localization sets for tensors and the applications in rank-one approximation and quantum entanglementhttps://zbmath.org/1517.150202023-09-22T14:21:46.120933Z"Zhang, Juan"https://zbmath.org/authors/?q=ai:zhang.juan.1|zhang.juan.2|zhang.juan.7"Chen, Xuechan"https://zbmath.org/authors/?q=ai:chen.xuechanSummary: In this paper, we propose two Z-eigenvalue inclusive sets of tensors, and prove that our new inclusion sets are more precise than some existing results. Using the derived inclusion sets, we present new upper and lower bounds of the spectral radius of nonnegative weakly symmetric tensors. Further, we offer two applications of the obtained upper and lower bounds. One application is the best rank-one approximation rate. The other application is the geometric measure of quantum pure state entanglement with nonnegative amplitudes. Finally, numerical examples are given to illustrate the validity of the derived results.Veronese and Segre morphisms between non-commutative projective spaceshttps://zbmath.org/1517.160262023-09-22T14:21:46.120933Z"Arici, Francesca"https://zbmath.org/authors/?q=ai:arici.francesca"Galuppi, Francesco"https://zbmath.org/authors/?q=ai:galuppi.francesco"Gateva-Ivanova, Tatiana"https://zbmath.org/authors/?q=ai:gateva-ivanova.tatianaSummary: We study Veronese and Segre morphisms between non-commutative projective spaces. We compute finite reduced Gröbner bases for their kernels, and compare them with their analogues in the commutative case.A wells type exact sequence for non-degenerate unitary solutions of the Yang-Baxter equationhttps://zbmath.org/1517.160292023-09-22T14:21:46.120933Z"Bardakov, Valeriy"https://zbmath.org/authors/?q=ai:bardakov.valerii-georgievich"Singh, Mahender"https://zbmath.org/authors/?q=ai:singh.mahenderThis paper is devoted to linear cycle sets which are closely related to set-theoretical solutions of the Yang-Baxter equation.
Let \(X\) be a set. Let \(r\colon X\times X\to X\times X\) be a map. Let \(r_{12},r_{23}\colon X\times X\times X\to X\times X\times X\) be the maps given respectively by \(r_{12}(x,y,z)=(r(x,y),z)\) and \(r_{23}(x,y,z)=(x,r(y,z))\). A pair \((X,r)\), where \(r\) is as above, is a \textit{set-theoretic solution} of the Yang-Baxter equation when \(r_{12}r_{23}r_{12}=r_{23}r_{12}r_{23}\). \(r\) then is \textit{non-degenerate} when the maps \(\pi_2\circ r(x,-)\colon X\to X\) and \(\pi_1\circ r(-,y)\colon X\to X\) are bijective for all \(x,y\in X\), where \(\pi_1,\pi_2\colon X\times X\to X\) are respectively the projections onto the first and the second factor.
A \textit{(left) cycle set} is a non-empty set \(X\) with a binary operation \(\cdot\) having bijective left translations \(x\mapsto y\cdot x\), and satisfying the equation \((x\cdot y)\cdot (x\cdot z)=(y\cdot x)\cdot (y\cdot z)\) for all \(x,y,z\in X\).
Cycle sets are in bijection with non-degenerate ``unitary'' set-theoretic solutions of the Yang-Baxter equation.
A \textit{(left) linear cycle set} is a cycle set \((X,\cdot)\) with an abelian group operation \(+\) such that \(\cdot\) is left distributive over \(+\) and such that \((x+y)\cdot z=(x\cdot y)\cdot (x\cdot z)\), \(x,y,z\in X\). E.g. any abelian group becomes a linear cycle set, called \textit{trivial}, when \((X,\cdot)\) is a right-zero band, that is, with \(x\cdot y=y\).
In this paper the authors, after recalling some notions about cohomology and about extensions of linear cycle sets, prove that there is a canonical group homomorphism between the second linear cycle set cohomology and the second symmetric cohomology of the underlying abelian group (Prop. 2.6), and, for trivial linear cycle sets, they show that this homomorphism is onto, and that in fact up to an isomorphism it is simply the projection onto the second factor (Prop. 2.7).
They also provide, for each central extension of linear cycle sets, a four term exact sequence in which occur group of \(1\)-cocyles, automorphism groups and second cohomology groups (Theorem 4.5).
Reviewer: Laurent Poinsot (Villetaneuse)Ghost center and representations of the diagonal reduction algebra of \(\mathfrak{osp}(1 | 2)\)https://zbmath.org/1517.170062023-09-22T14:21:46.120933Z"Hartwig, Jonas T."https://zbmath.org/authors/?q=ai:hartwig.jonas-t"Williams, Dwight Anderson II"https://zbmath.org/authors/?q=ai:williams.dwight-anderson-iiSummary: Reduction algebras are known by many names in the literature, including step algebras, Mickelsson algebras, Zhelobenko algebras, and transvector algebras, to name a few. These algebras, realized by raising and lowering operators, allow for the calculation of Clebsch-Gordan coefficients, branching rules, and intertwining operators; and have connections to extremal equations and dynamical R-matrices in integrable face models.
In this paper we continue the study of the diagonal reduction superalgebra \(A\) of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(1 | 2)\). We construct a Harish-Chandra homomorphism, Verma modules, and study the Shapovalov form on each Verma module. Using these results, we prove that the ghost center (center plus anti-center) of \(A\) is generated by two central elements and one anti-central element (analogous to the Scasimir due to Leśniewski for \(\mathfrak{osp}(1 | 2))\). As another application, we classify all finite-dimensional irreducible representations of \(A\). Lastly, we calculate an infinite-dimensional tensor product decomposition explicitly.Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equationhttps://zbmath.org/1517.170152023-09-22T14:21:46.120933Z"Catino, Francesco"https://zbmath.org/authors/?q=ai:catino.francesco"Mazzotta, Marzia"https://zbmath.org/authors/?q=ai:mazzotta.marzia"Stefanelli, Paola"https://zbmath.org/authors/?q=ai:stefanelli.paolaThis paper aims to show how to obtain weak braces from Rota-Baxter operators defined on Clifford semigroups, for which the authors introduce the notion of Rota-Baxter operator on a Clifford semigroup \(\left(S,+\right)\), i.e., a map
\[
\mathfrak{R}:S\rightarrow S
\]
abiding by the relations
\begin{align*}
\mathfrak{R}\left(a\right)+\mathfrak{R}\left(b\right) & =\left(a+\mathfrak{R}\left(a\right)+b-\mathfrak{R}\left(a\right)\right)\\
a+\mathfrak{R}\left(a\right)-\mathfrak{R}\left(a\right) & =a
\end{align*}
for all \(a,b\in S\).
The synopsis of the paper goes as follows.
\begin{itemize}
\item[\S 1] gives essential results on the structures of weak braces introduced in [\textit{F. Catino} et al., Semigroup Forum 104, No. 2, 228--255 (2022; Zbl 07533946)] to find solutions of the Yang-Baxter equation. Some basics on Clifford semigroups are recalled [\textit{A. H. Clifford} and \textit{G. B. Preston}, The algebraic theory of semigroups. Vol. I. Providence, RI: American Mathematical Society (AMS) (1961; Zbl 0111.03403); \textit{G. Cooperman} and \textit{L. Finkelstein}, J. Symb. Comput. 17, No. 6, 513--528 (1994; Zbl 0835.20007); \textit{M. Petrich}, Inverse semigroups. Pure and Applied Mathematics. A Wiley-Interscience Publication. New York etc.: John Wiley \& Sons. (1984; Zbl 0546.20053)].
\item[\S 2] presents and investigates the Rota-Baxter operators on a Clifford semigroup, consistently with that introduced for groups in [\textit{L. Guo} et al., Adv. Math. 387, Article ID 107834, 34 p. (2021; Zbl 1468.17026)].
\item[\S 3] focuses on Rota-Baxter endomorphisms, giving a description of such maps \(f\) for which \(\mathrm{Im}\,f\) is commutative. The authors characterize Rota-Baxter endomorphisms of groups that are also idempotents.
\item[\S 4] illustrates a method for obtaining a dual weak brace \(S\) starting from a given Rota-Baxter operator on a Clifford semigroup \(\left(S,+\right) \). The construction is inspired by that of skew braces due to \textit{V. G. Bardakov} and \textit{V. Gubarev} [J. Algebra 596, 328--351 (2022; Zbl 1492.17019), Proposition 3.1]. It is shown that every commutative Rota-Baxter endormorphism determines a bi-weak brace.
\item[\S 5] makes explicit the solutions associated to dual weak braces obtained through Rota-Baxter operators.
\item[\S 6] deals with the ideals of a dual weak brace, by extending the already known theory for skew braces. In particular, the notion of the socle of a dual weak brace is introduced. The ideals of dual weak braces associated to a given Rota-Baxter operator are finally described.
\end{itemize}
Reviewer: Hirokazu Nishimura (Tsukuba)Connections between vector-valued and highest weight Jack and Macdonald polynomialshttps://zbmath.org/1517.330072023-09-22T14:21:46.120933Z"Colmenarejo, Laura"https://zbmath.org/authors/?q=ai:colmenarejo.laura"Dunkl, Charles F."https://zbmath.org/authors/?q=ai:dunkl.charles-f"Luque, Jean-Gabriel"https://zbmath.org/authors/?q=ai:luque.jean-gabrielSummary: We analyze conditions under which a projection from the vector-valued Jack or Macdonald polynomials to scalar polynomials has useful properties, specially commuting with the actions of the symmetric group or Hecke algebra, respectively, and with the Cherednik operators for which these polynomials are eigenfunctions. In the framework of representation theory of the symmetric group and the Hecke algebra, we study the relation between singular nonsymmetric Jack and Macdonald polynomials and highest weight symmetric Jack and Macdonald polynomials. Moreover, we study the quasistaircase partition as a continuation of our study on the conjectures of Bernevig and Haldane on clustering properties of symmetric Jack polynomials.The heat kernel on the diagonal for a compact metric graphhttps://zbmath.org/1517.340382023-09-22T14:21:46.120933Z"Borthwick, David"https://zbmath.org/authors/?q=ai:borthwick.david"Harrell, Evans M. II"https://zbmath.org/authors/?q=ai:harrell.evans-m-ii"Jones, Kenny"https://zbmath.org/authors/?q=ai:jones.kennySummary: We analyze the heat kernel associated with the Laplacian on a compact metric graph, with standard Kirchhoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin-Potthoff-Schrader, allows for a straightforward analysis of small-time asymptotics. We show that the restriction of the heat kernel to the diagonal satisfies a modified version of the heat equation. This observation leads to an ``edge'' heat trace formula, expressing the a sum over eigenfunction amplitudes on a single edge as a sum over closed loops containing that edge. The proof of this formula relies on a modified heat equation satisfied by the diagonal restriction of the heat kernel. Further study of this equation leads to explicit formulas for graphs which are symmetric about each vertex.Van der Waals interactions between two hydrogen atoms: the next ordershttps://zbmath.org/1517.351892023-09-22T14:21:46.120933Z"Cancès, Eric"https://zbmath.org/authors/?q=ai:cances.eric"Coyaud, Rafaël"https://zbmath.org/authors/?q=ai:coyaud.rafael"Scott, L. Ridgway"https://zbmath.org/authors/?q=ai:scott.larkin-ridgwaySummary: We extend a method [\textit{E. Cancès} and \textit{L. R. Scott}, SIAM J. Math. Anal. 50, No. 1, 381--410 (2018; Zbl 1386.35363)] to compute more terms in the asymptotic expansion of the van der Waals attraction between two hydrogen atoms. These terms are obtained by solving a set of modified Slater-Kirkwood partial differential equations. The accuracy of the method is demonstrated by numerical simulations and comparison with other methods from the literature. It is also shown that the scattering states of the hydrogen atom, that are the states associated with the continuous spectrum of the Hamiltonian, have a major contribution to the C\(_6\) coefficient of the van der Waals expansion.Efficient manipulation of Bose-Einstein condensates in a double-well potentialhttps://zbmath.org/1517.351992023-09-22T14:21:46.120933Z"Adriazola, Jimmie"https://zbmath.org/authors/?q=ai:adriazola.jimmie"Goodman, Roy"https://zbmath.org/authors/?q=ai:goodman.roy-h"Kevrekidis, Panayotis"https://zbmath.org/authors/?q=ai:kevrekidis.panayotis-gSummary: We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including \textit{three} modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.Darboux transformations for the \(\hat{A}_{2n}^{(2)}\)-KdV hierarchyhttps://zbmath.org/1517.370732023-09-22T14:21:46.120933Z"Terng, Chuu-Lian"https://zbmath.org/authors/?q=ai:terng.chuu-lian"Wu, Zhiwei"https://zbmath.org/authors/?q=ai:wu.zhiweiAuthors' abstract: The \(\hat{A}^{(2)}_{2n}\)-hierarchy can be constructed from a splitting of the Kac-Moody algebra of type \(\hat{A}^{(1)}_{2n}\) by an involution. By choosing certain cross section of the gauge action, we obtain the \(\hat{A}^{(2)}_{2n}\)-KdV hierarchy. They are the equations for geometric invariants of isotropic curve flows of type A, which gives a geometric interpretation of the soliton hierarchy. In this paper, we construct Darboux and Bäcklund transformations for the \(\hat{A}^{(2)}_{2n}\)-hierarchy, and use it to construct Darboux transformations for the \(\hat{A}^{(2)}_{2n}\)-KdV hierarchy and isotropic curve flows of type A. Moreover, explicit soliton solutions for these hierarchies are given.
Reviewer: Ti-Jun Xiao (Fudan)Frame potential in \(CP^n\) some numerical and analytical resultshttps://zbmath.org/1517.420292023-09-22T14:21:46.120933Z"Ben Av, Radel"https://zbmath.org/authors/?q=ai:ben-av.radel"Dula, Giora"https://zbmath.org/authors/?q=ai:dula.giora"Goldberger, Assaf"https://zbmath.org/authors/?q=ai:goldberger.assaf"Strassler, Yossi"https://zbmath.org/authors/?q=ai:strassler.yossiThe article explores the problem of minimizing the Frame Potential in complex projective spaces. The authors highlight that the minimization of the energy functional has been a longstanding pursuit in both numerical and analytical research, with recent advancements in this field. They emphasize the relevance of complex spaces, particularly \(CP^n\) spaces, in the context of Quantum Mechanics, which has spurred growing interest.
The paper focuses on Frame Potentials. Given a configuration of \(m\) unit vectors \(v_1, \ldots, v_m \in \mathbb{C}^n\), their Frame Potential is defined as \[ \Phi_p\left(v_1, \ldots, v_m\right)=\sum_{1 \leq i<j \leq m}\left|\left\langle v_i, v_j\right\rangle\right|^p. \] The authors discuss solutions for a minimization of the frame potential problem in \(C P^n\).
Reviewer: Pierluigi Vellucci (Roma)On the continuous frame quantum detection problemhttps://zbmath.org/1517.420302023-09-22T14:21:46.120933Z"Hong, Guoqing"https://zbmath.org/authors/?q=ai:hong.guoqing"Li, Pengtong"https://zbmath.org/authors/?q=ai:li.pengtongPositive operator-valued measures (POVMs) play an important role in quantum detection where one has to recover a state from a collection of measurements from the system on this state. If a POVM can uniquely determine a state, it is called informationally complete. In the quantum detection problem, one seeks to characterize POVMs that are informationally complete. A quantum injective frame is a frame that can be used to distinguish states from their frame measurements, and the frame quantum detection problem seeks to characterize all such frames. Other authors have given some characterizations for the trace class and the Hilbert-Schmidt class injective continuous frames. In this paper, the authors present several characterizations for Schatten \(p\)-class injective continuous frames in terms of discrete representations of continuous frames, where \(1 \leq p < \infty\). In that respect, the quantum detection problem is investigated in the general setting, and this work expands the scope of solutions to the quantum detection problem.
Reviewer: Somantika Datta (Moscow, ID)Counterexamples to the extendibility of positive unital norm-one mapshttps://zbmath.org/1517.460372023-09-22T14:21:46.120933Z"Chiribella, Giulio"https://zbmath.org/authors/?q=ai:chiribella.giulio"Davidson, Kenneth R."https://zbmath.org/authors/?q=ai:davidson.kenneth-r"Paulsen, Vern I."https://zbmath.org/authors/?q=ai:paulsen.vern-ival"Rahaman, Mizanur"https://zbmath.org/authors/?q=ai:rahaman.mizanurSummary: Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by positivity is known to be false. A natural question is whether extendibility could still hold for positive maps satisfying stronger conditions, such as being unital and norm 1. Here we provide three counterexamples showing that positive norm-one unital maps defined on an operator subsystem of a matrix algebra cannot be extended to a positive map on the full matrix algebra. The first counterexample is an unextendible positive unital map with unit norm, the second counterexample is an unextendible positive unital isometry on a real operator space, and the third counterexample is an unextendible positive unital isometry on a complex operator space.On the structure of the field \(C^\ast \)-algebra of a symplectic space and spectral analysis of the operators affiliated to ithttps://zbmath.org/1517.460512023-09-22T14:21:46.120933Z"Georgescu, Vladimir"https://zbmath.org/authors/?q=ai:georgescu.vladimir"Iftimovici, Andrei"https://zbmath.org/authors/?q=ai:iftimovici.andreiSummary: We show that the \(C^\ast \)-algebra generated by the field operators associated to a symplectic space \(\Xi\) is graded by the semilattice of all finite dimensional subspaces of \(\Xi \). If \(\Xi\) is finite dimensional we give a simple intrinsic description of the components of the grading, we show that the self-adjoint operators affiliated to the algebra have a many channel structure similar to that of \(N\)-body Hamiltonians, in particular their essential spectrum is described by a kind of HVZ theorem, and we point out a large class of operators affiliated to the algebra.Infinite quantum permutationshttps://zbmath.org/1517.460522023-09-22T14:21:46.120933Z"Voigt, Christian"https://zbmath.org/authors/?q=ai:voigt.christianSummary: We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by \textit{S.-Z. Wang} [Commun. Math. Phys. 195, No.~1, 195--211 (1998; Zbl 1013.17008)]. More precisely, the resulting quantum groups encode universal quantum symmetries of the underlying sets among all discrete quantum groups. We also discuss quantum automorphisms of infinite graphs, including some examples and open problems regarding both the existence and non-existence of quantum symmetries in this setting.The \(L^p\) boundedness of the wave operators for matrix Schrödinger equationshttps://zbmath.org/1517.470752023-09-22T14:21:46.120933Z"Weder, Ricardo"https://zbmath.org/authors/?q=ai:weder.ricardo-aSummary: We prove that the wave operators for \(n \times n\) matrix Schrödinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces \(L^p (\mathbb{R}^+, \mathbb{C}^n)\), \( 1 < p < \infty\), for slowly decaying selfadjoint matrix potentials \(V\) that satisfy the condition \(\int_0^{{\infty}} (1 + x) |V (x)| \,d x < {\infty}\). Moreover, assuming that \(\int_0^{{\infty}} (1 + x^\gamma) |V (x)|\,d x < {\infty}\), \(\gamma > \frac{5}{2}\), and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in \(L^1 (\mathbb{R}^+, \mathbb{C}^n)\) and in \(L^{{\infty}} (\mathbb{R}^+, \mathbb{C}^n)\). We also prove that the wave operators for \(n \times n\) matrix Schrödinger equations on the line are bounded in the spaces \(L^p (\mathbb{R}, \mathbb{C}^n)\), \(1 < p < {\infty}\), assuming that the perturbation consists of a point interaction at the origin and of a potential \(\mathcal{V}\) that satisfies the condition \(\int_{-\infty}^{\infty} (1+|x|)|\mathcal{V}(x)|\, dx<\infty\). Further, assuming that \(\int_{-\infty}^{\infty} (1+|x|^\gamma)|\mathcal{V}(x)| \,dx<\infty\), \(\gamma > \frac{5}{2}\), and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in \(L^1 (\mathbb{R}, \mathbb{C}^n)\) and in \(L^{{\infty}} (\mathbb{R}, \mathbb{C}^n)\). We obtain our results for \(n \times n\) matrix Schrödinger equations on the line from the results for \(2 n \times 2 n\) matrix Schrödinger equations on the half line.Norm-ideal perturbations of one-parameter semigroups and applicationshttps://zbmath.org/1517.470772023-09-22T14:21:46.120933Z"Boulton, Lyonell"https://zbmath.org/authors/?q=ai:boulton.lyonell"Dimoudis, Spyridon"https://zbmath.org/authors/?q=ai:dimoudis.spyridonFirstly, the authors examine a general framework for perturbation of generators relative to the Schatten-von Neumann ideals on Hilbert spaces, obtaining in this way a development for a family of equivalence relations on generators. Also, they prove applications of the abstract setting to heat semigroups associated with nonselfadjoint Schrödinger operators.
Reviewer: Elhadj Dahia (Bou Saâda)A QP perspective on topology change in Poisson-Lie T-dualityhttps://zbmath.org/1517.530752023-09-22T14:21:46.120933Z"Arvanitakis, Alex S."https://zbmath.org/authors/?q=ai:arvanitakis.alex-s"Blair, Chris D. A."https://zbmath.org/authors/?q=ai:blair.chris-d-a"Thompson, Daniel C."https://zbmath.org/authors/?q=ai:thompson.daniel-cThis paper is devoted to the global fibration structure under Poisson-Lie T-duality in terms of differential graded symplectic QP manifolds and their canonical transformations.
The authors describe:
(1) The \(T\)-duality in terms of correspondences as the fibered product
\[\mathbb D\hookrightarrow \mathbb M = M \times_B \widetilde{M} \longrightarrow B\]
of two QP manifolds \(\mathcal M\) and \(\widetilde{\mathcal M}\) with Lie group left/right actions \(G\) and \(\widetilde{G}\), respectively. When the base \(B\) is reduced to a point, this is exactly the Drinfeld double;
(2) A sufficient condition that ensures that \(\mathbb M\) is a bibundle.
As an application the authors reduce the T-duality to the duality of worldsheet sigma models in their Hamiltonian formulation and deduce formulas for the transformation of Ramond-Ramond fluxes under Poisson-Lie T-duality in the case of spectators. The canonical transformations appearing in the reduction procedure suggest a Fourier-Mukai integral transformation for Poisson-Lie T-duality.
Reviewer: Do Ngoc Diep (Hanoi)High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouvillehttps://zbmath.org/1517.651012023-09-22T14:21:46.120933Z"Chen, Shi"https://zbmath.org/authors/?q=ai:chen.shi"Ding, Zhiyan"https://zbmath.org/authors/?q=ai:ding.zhiyan"Li, Qin"https://zbmath.org/authors/?q=ai:li.qin"Zepeda-Núñez, Leonardo"https://zbmath.org/authors/?q=ai:zepeda-nunez.leonardoSummary: We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models in the high-frequency limit. In particular, we evaluate the asymptotic convergence of a generalized version of the inverse scattering problem based on the Helmholtz equation, to the inverse scattering problem of the Liouville equation (a simplified version of RTE). The two inverse problems are connected through the Wigner transform that translates the wave-type description on the physical space to the kinetic-type description on the phase space, and the Husimi transform that models data localized both in location and direction. The finding suggests that impinging tightly concentrated monochromatic beams can indeed provide stable reconstruction of the medium, asymptotically in the high-frequency regime. This fact stands in contrast with the unstable reconstruction for the classical inverse scattering problem when the probing signals are plane waves.The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problemhttps://zbmath.org/1517.651032023-09-22T14:21:46.120933Z"Henning, Patrick"https://zbmath.org/authors/?q=ai:henning.patrickSummary: In this paper, we consider the generalized inverse iteration for computing ground states of the Gross-Pitaevskii eigenvector (GPE) problem. For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross-Pitaevskii operator, recovering the same rates as for linear eigenvector problems. With this we establish the first local convergence result for the basic inverse iteration for the GPE without damping. We also show how our findings directly generalize to extended inverse iterations, such as the Gradient Flow Discrete Normalized (GFDN) proposed in [\textit{W. Bao} and \textit{Q. Du}, SIAM J. Sci. Comput. 25, No. 5, 1674--1697 (2004; Zbl 1061.82025)] or the damped inverse iteration suggested in our paper with \textit{D. Peterseim} [SIAM J. Numer. Anal. 58, No. 3, 1744--1772 (2020; Zbl 1512.35538)]. Our analysis also reveals why the inverse iteration for the GPE does not react favorably to spectral shifts. This empirical observation can now be explained with a blow-up of a weighting function that crucially contributes to the convergence rates. Our findings are illustrated by numerical experiments.Finite-temperature field theory. Principles and applicationshttps://zbmath.org/1517.700012023-09-22T14:21:46.120933Z"Kapusta, Joseph I."https://zbmath.org/authors/?q=ai:kapusta.joseph-i"Gale, Charles"https://zbmath.org/authors/?q=ai:gale.charlesThis book develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Specific physical theories treated include QED, QCD, electroweak theory, and effective nuclear field theories of hadronic and nuclear matter. Topics covered include: functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and plasma oscillations, spontaneous symmetry breaking, Goldstone theorem, resummation and hard thermal loops, lattice gauge theory, phase transitions, nucleation theory, quark-gluon plasma, and color superconductivity. Applications to astrophysics and cosmology cover white dwarf and neutron stars, neutrino emissivity, baryon number violation in the early universe, and cosmological phase transitions. Applications to relativistic nucleus-nucleus collisions are also included. The book is written for theorists in elementary particle physics, nuclear physics, astrophysics, and cosmology. Released initially in 2006, this title has been reissued as an Open Access publication on Cambridge Core.
See the reviews of the first paperback edition and the 2006 second hardback edition in [Zbl 0805.70003; Zbl 1121.70002]. For the first hardback edition and the second paperback edition see [Zbl 0743.70020; Zbl 1215.70002].Out-of-plane enhancement in a discrete random halfspacehttps://zbmath.org/1517.780042023-09-22T14:21:46.120933Z"McCargar, Reid K."https://zbmath.org/authors/?q=ai:mccargar.reid-k"Lang, Roger H."https://zbmath.org/authors/?q=ai:lang.roger-henryThe authors develop the heuristic radiative transfer theory concerning waves propagating in a random medium modeled by particles independently and identically distributed throughout the slab. The model is based on the Helmholtz equation. The authors investigate the mean-wave Green's function.
Reviewer: Vladimir Mityushev (Kraków)An introduction to the standard model of particle physics.https://zbmath.org/1517.810012023-09-22T14:21:46.120933Z"Cottingham, W. Noel"https://zbmath.org/authors/?q=ai:cottingham.w-noel"Greenwood, Derek A."https://zbmath.org/authors/?q=ai:greenwood.derek-aPublisher's description: The second edition of this introductory graduate textbook provides a concise yet accessible introduction to the Standard Model. It has been updated to account for the successes of the theory of strong interactions and the observations on matter-antimatter asymmetry. It gives a coherent presentation of the phenomena and theory that describe neutrino mass as well as an account of progress in the theory of strong interactions. The book develops clearly the theoretical concepts from the electromagnetic and weak interactions of leptons and quarks to the strong interactions of quarks. Each chapter ends with problems, with hints to selected problems provided at the end of the book. The mathematical treatments are suitable for graduates in physics, while more sophisticated mathematical ideas are developed in the text and appendices. First published in 2007, this title has been reissued as an Open Access publication on Cambridge Core.
See the review of the original second edition in [Zbl 1126.81002]. For the review of the first edition see [Zbl 0965.81136].Symmetry, broken symmetry, and topology in modern physics. A first coursehttps://zbmath.org/1517.810022023-09-22T14:21:46.120933Z"Guidry, Mike"https://zbmath.org/authors/?q=ai:guidry.mike"Sun, Yang"https://zbmath.org/authors/?q=ai:sun.yangPublisher's description: Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.Quantized detector networks. The theory of observationhttps://zbmath.org/1517.810032023-09-22T14:21:46.120933Z"Jaroszkiewicz, George"https://zbmath.org/authors/?q=ai:jaroszkiewicz.georgeFor the original edition see [Zbl 1376.81002].Introduction to quantum fields on a lattice. ``A robust mate''https://zbmath.org/1517.810042023-09-22T14:21:46.120933Z"Smit, Jan"https://zbmath.org/authors/?q=ai:smit.jan-c|smit.jan-w-aPublisher's description: This book provides a concise introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as `triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-Abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.
See the review of the 2002 edition in [Zbl 1021.81043].The Lund modelhttps://zbmath.org/1517.810052023-09-22T14:21:46.120933Z"Andersson, Bo"https://zbmath.org/authors/?q=ai:andersson.boThe Lund model, inspired by quantum chromodynamics, has provided a promising approach to the dynamics of quark and gluon interactions. Starting with a brief reprise of basic concepts in relativity, quantum mechanics of fields and particle physics, this book discusses: the dynamics of the massless relativistic string; confinement; causality and relativistic covariance; Lund fragmentation processes; QED and QCD Bremsstrahlung; multiplicities and particle-parton distributions. Throughout the book, theory is confronted with current experimental data, and implications for future experiments are also considered. The book also explores the relationships between the Lund model and other models based on field theory (the Schwinger model, S-matrix models, light-cone algebra physics and variations of the parton model), and models based on statistical mechanics (the Feynman-Wilson gas, scaling, iterative cascade models). This title, first published in 1998, has been reissued as an Open Access publication on Cambridge Core.
See the review of the original edition in [Zbl 0943.81001].Renormalization. An introduction to renormalization, the renormalization group, and the operator-product expansionhttps://zbmath.org/1517.810062023-09-22T14:21:46.120933Z"Collins, John C."https://zbmath.org/authors/?q=ai:collins.john-cPublisher's description: Many numerical predictions of experimental phenomena in particle physics are made possible by exploiting the discovery that simplifications can happen when phenomena are investigated on short distance and time scales. This book provides a coherent exposition of the renormalization techniques underlying these calculations. After reminding the reader of some basic properties of field theories, examples are used to explain the problems to be treated. The technique of dimensional regularization and the renormalization group is then shown. Finally a number of key applications are demonstrated, culminating in the treatment of deeply inelastic scattering. Originally published in 1984, this title has been reissued as an Open Access publication on Cambridge Core.
See the review of the original paperback edition in [Zbl 0614.53060]. For the original hardback edition see [Zbl 1094.53505].Non-perturbative field theory. From two dimensional conformal field theory to QCD in four dimensionshttps://zbmath.org/1517.810072023-09-22T14:21:46.120933Z"Frishman, Yitzhak"https://zbmath.org/authors/?q=ai:frishman.yitzhak"Sonnenschein, Jacob"https://zbmath.org/authors/?q=ai:sonnenschein.jacobPublisher's description: Providing a new perspective on quantum field theory, this book gives a pedagogical exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research in theoretical physics. After describing non-perturbative methods in detail, it uses these methods to explore two-dimensional and four-dimensional gauge dynamics. The book concludes with a summary emphasizing the interplay between two- and four-dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and `t Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics in particular, are thoroughly described. Published originally in 2010, this title has been reissued as an Open Access publication on Cambridge Core.
See the review of the 2010 edition in [Zbl 1213.81007].Supersymmetric solitonshttps://zbmath.org/1517.810082023-09-22T14:21:46.120933Z"Shifman, Misha"https://zbmath.org/authors/?q=ai:shifman.mikhail-a"Yung, A."https://zbmath.org/authors/?q=ai:yung.alexeiPublisher's description: In the last decade methods and techniques based on supersymmetry have provided deep insights in quantum chromodynamics and other non-supersymmetric gauge theories at strong coupling. This book summarizes major advances in critical solitons in supersymmetric theories, and their implications for understanding basic dynamical regularities of non-supersymmetric theories. After an extended introduction on the theory of critical solitons, including a historical introduction, the authors focus on three topics: non-Abelian strings and confined monopoles; reducing the level of supersymmetry; and domain walls as D-brane prototypes. They also provide a thorough review of issues at the cutting edge, such as non-Abelian flux tubes. The book presents an extensive summary of the current literature so researchers in this field can understand the background and related issues. First published in 2009, this title has been reissued as an Open Access publication on Cambridge Core.
See the review of the original edition in [Zbl 1182.81003].18th conference on the theory of quantum computation, communication and cryptography, TQC 2023, Aveiro, Portugal, July 24--28, 2023https://zbmath.org/1517.810092023-09-22T14:21:46.120933ZThe articles of this volume will be reviewed individually. For the preceding conference see [Zbl 1491.81011].Quantumness of qubit states interacting with two structured reservoirs in indefinite causal orderhttps://zbmath.org/1517.810102023-09-22T14:21:46.120933Z"Ban, Masashi"https://zbmath.org/authors/?q=ai:ban.masashiSummary: Quantumness is studied for single and bipartite states of qubits which interact with the identical structured reservoirs in indefinite causal order. Coherence and temporal steerability are investigated for a single-qubit state. Entanglement, spatial steerability and the Bell-CHSH nonlocality are examined for a bipartite-qubit state. It is shown that the indefinite causal order can reduce the decay of the quantumness of qubit states.Is time a cyclic dimension? Canonical quantization implicit in classical cyclic dynamicshttps://zbmath.org/1517.810112023-09-22T14:21:46.120933Z"Dolce, Donatello"https://zbmath.org/authors/?q=ai:dolce.donatelloSummary: If ``quantization is an art'' then it can be greatly refined by adopting cyclic time formalism. In past papers we have proven the effectiveness of a formulation of physics based on cyclic relativistic time. Now we are able to demonstrate in a general way, by using theorems of Geometric Quantization, that the Poisson brackets of intrinsically \textit{cyclic} time dynamics directly imply the ordinary canonical commutation relations and the other Dirac's rules of canonical Quantum Mechanics. In other words, according to our result, the canonical quantization is an implicit way of imposing intrinsically cyclic time dynamics without explicitly saying that time is a cyclic dimension.Is the statistical interpretation of quantum mechanics \(\psi\)-ontic or \(\psi\)-epistemic?https://zbmath.org/1517.810122023-09-22T14:21:46.120933Z"Hubert, Mario"https://zbmath.org/authors/?q=ai:hubert.marioSummary: The ontological models framework distinguishes \(\psi\)-ontic from \(\psi\)-epistemic wave-functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it \(\psi\)-epistemic and incomplete or \(\psi\)-ontic and complete? I will argue that the wave-function in this interpretation is best regarded as \(\psi\)-ontic \textit{and incomplete}.Aspects of superdeterminism made intuitivehttps://zbmath.org/1517.810132023-09-22T14:21:46.120933Z"Nikolaev, Vitaly"https://zbmath.org/authors/?q=ai:nikolaev.vitaly"Vervoort, Louis"https://zbmath.org/authors/?q=ai:vervoort.louisSummary: We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial `bang' correlates all events, just as in the superdeterministic universe. We introduce the notions of `strong' and `soft' superdeterminism, in order to clarify debates in the literature. Based on the analogy with billiards, we show that superdeterministic correlations may exist as a matter of principle, but be undetectable for all practical purposes. Even if inaccessible, such strong-superdeterministic correlations can explain why soft-, or effective, superdeterministic theories can be built. We counter classic objections to superdeterminism such as the claim that it would be at odds with the scientific method, and with the construction of new theories. Finally, we show that probability theory, as a physical theory, indicates that superdeterminism has a greater explanatory power than its competitors: it can coherently answer questions from probability theory for which other positions remain powerless. Since probability theory is, in a sense, the most unifying physics theory (all physical systems comply with it), this argument confers considerable weight.BV quantisation in perturbative algebraic QFT: fundamental concepts and perspectiveshttps://zbmath.org/1517.810142023-09-22T14:21:46.120933Z"Rejzner, Kasia"https://zbmath.org/authors/?q=ai:rejzner.katarzynaSummary: This chapter is mainly based on the talk presented at the meeting The Philosophy and Physics of Noether's Theorems that took place 5-6 October 2018, but it also contains some original results that were inspired by discussions with mathematicians, physicists, and philosophers about the problem of understanding the intrinsic meaning of gauge invariance. Following the principles of locality, deformation, and homology, one naturally ends up using the Batalin-Vilkovisky (BV) formalism in quantizing gauge theories. Beginning with the gentle introduction into the BV framework, the chapter proceeds to some new results and more speculative deliberations. In the classical theory, a new perspective is presented on the classical BV operator, using the notion of Møller maps. In the quantum theory, some loose ideas are presented on the formulation of anomalous master Ward identity in the framework proposed recently by Buchholz and Fredenhagen, based on local S-matrices.
For the entire collection see [Zbl 1497.37002].Relating Hilbert-Chu correspondences and big toy models for quantum mechanicshttps://zbmath.org/1517.810152023-09-22T14:21:46.120933Z"Krídlo, O."https://zbmath.org/authors/?q=ai:kridlo.ondrej"Ojeda-Aciego, M."https://zbmath.org/authors/?q=ai:ojeda-aciego.manuelSummary: In a previous work, we showed that the category \(\mathrm{ChuCors}_{\mathcal{H}}\) of Chu correspondences between Hilbert contexts is equivalent to the category of Propositional Systems (the algebraic counterpart of the set of closed subspaces of a Hilbert space); in this paper, we extend the previous relation to the Big Toy Models introduced as a tool to represent quantum systems in terms of Chu spaces.
For the entire collection see [Zbl 1415.68006].Response to: ``Comment on: ``Do Bloch waves interfere with one another ?''''https://zbmath.org/1517.810162023-09-22T14:21:46.120933Z"Vyas, Vivek M."https://zbmath.org/authors/?q=ai:vyas.vivek-mSummary: Here a generalised argument showing the existence of the Bloch superselection rule is presented, in response to the recent comment by \textit{T. Sowiński} [Phys. Lett., A 456, Article ID 128198, 2 p. (2022; Zbl 1515.81037)]. In light of the role played by the periodic boundary condition, locality and topology in the system, the claim made in the comment is found untenable.Local approach to quantum-inspired classificationhttps://zbmath.org/1517.810172023-09-22T14:21:46.120933Z"Blanzieri, Enrico"https://zbmath.org/authors/?q=ai:blanzieri.enrico"Leporini, Roberto"https://zbmath.org/authors/?q=ai:leporini.roberto"Pastorello, Davide"https://zbmath.org/authors/?q=ai:pastorello.davideSummary: In the context of quantum-inspired machine learning, remarkable mathematical tools for solving classification problems are given by some methods of quantum state discrimination. In this respect, quantum-inspired classifiers based on nearest centroid and Helstrom discrimination have been efficiently implemented on classical computers. We present a local approach combining the kNN algorithm to some quantum-inspired classifiers.A brief journey through collision models for multipartite open quantum dynamicshttps://zbmath.org/1517.810182023-09-22T14:21:46.120933Z"Cattaneo, Marco"https://zbmath.org/authors/?q=ai:cattaneo.marco-e-g-v"Giorgi, Gian Luca"https://zbmath.org/authors/?q=ai:giorgi.gian-luca"Zambrini, Roberta"https://zbmath.org/authors/?q=ai:zambrini.roberta"Maniscalco, Sabrina"https://zbmath.org/authors/?q=ai:maniscalco.sabrinaSummary: The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed ``ancillas''. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.Entangled state distillation from single copy mixed states beyond LOCChttps://zbmath.org/1517.810192023-09-22T14:21:46.120933Z"Biswas, Indranil"https://zbmath.org/authors/?q=ai:biswas.indranil|biswas.indranil.1"Bhunia, Atanu"https://zbmath.org/authors/?q=ai:bhunia.atanu"Chattopadhyay, Indrani"https://zbmath.org/authors/?q=ai:chattopadhyay.indrani"Sarkar, Debasis"https://zbmath.org/authors/?q=ai:sarkar.debasisSummary: No pure entangled state can be distilled from a \(2 \otimes 2\) or \(2 \otimes 3\) mixed state by separable operations. In \(3 \otimes 3\), pure entanglement can be distilled by separable operation but not by LOCC. In this letter, we proved the conjecture [\textit{E. Chitambar} and \textit{R. Duan}, Phys. Rev. Lett. 103, No. 11, Article ID 110502, 4 p. (2009; \url{doi:10.1103/PhysRevLett.103.110502})] that it is possible to distill pure entanglement for \(2 \otimes 4\) system by LOCC and further improve these in higher dimensions to distill a pure entangled state of Schmidt rank \(d\) from a \(m \otimes n\) mixed state by separable operation when \(m + n \geqslant 3 d\). We found results for tripartite systems with target state \(d\)-level GHZ-type state. These results provide a class of systems where separable operation is strictly stronger than LOCC.Quantum dynamics of a f-deformed opto-mechanical systemhttps://zbmath.org/1517.810202023-09-22T14:21:46.120933Z"Dehghani, A."https://zbmath.org/authors/?q=ai:dehghani.alireza"Mojaveri, B."https://zbmath.org/authors/?q=ai:mojaveri.b"Aryaie, M."https://zbmath.org/authors/?q=ai:aryaie.mSummary: Based on the f-oscillator formalism, we introduce a nonlinear optomechanical framework which is constructed from the standard optomechanical system by deforming the single-mode photonic-field operators. Such a generalized optomechanical system describes an intensity-dependent interaction of a mechanical oscillator with a single-mode electromagnetic field. To gain insight into the effectiveness of the non-linearization processes, we investigate the role of the involving parameters especially the nonlinearity function that controls the entanglement and statistical properties of the photon-phonon state was considered. Thus, we apply the linear entropy measure and the Wigner function to quantify the entanglement and non-classical properties of this composite system and the condition in which quantum entanglement and negativity of the Wigner function can be enhanced and maximized has been identified. Thus, depending on an election of the nonlinearity function, one can observe different non-classical effects. These trends are compared with those obtained for the standard optomechanical system including photon-phonon interaction, too.Criteria of genuine multipartite entanglement based on correlation tensorshttps://zbmath.org/1517.810212023-09-22T14:21:46.120933Z"Jing, Naihuan"https://zbmath.org/authors/?q=ai:jing.naihuan"Zhang, Meiming"https://zbmath.org/authors/?q=ai:zhang.meimingSummary: We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems.Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure stateshttps://zbmath.org/1517.810222023-09-22T14:21:46.120933Z"Maziero, Jonas"https://zbmath.org/authors/?q=ai:maziero.jonas"Basso, Marcos L. W."https://zbmath.org/authors/?q=ai:basso.marcos-l-w"Céleri, Lucas C."https://zbmath.org/authors/?q=ai:celeri.lucas-cSummary: Complete complementarity relations, as e.g. \(P(\rho_A)^2 + C(\rho_A)^2 + E(|\Psi\rangle_{AB})^2 = 1\), constrain the local predictability and local coherence and the entanglement of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in [\textit{M. L. W. Basso} and \textit{J. Maziero}, Phys. Lett., A 451, Article ID 128414, 5 p. (2022; Zbl 1511.81023)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-basis measurement of the entanglement swapping protocol (ESP). In this article, we extend this result for general pure initial states. We obtain a general relation between pre-measurement local predictability and coherence and the distributed entanglement in the ESP. We use IBM's quantum computers to verify experimentally some instances of these general theoretical results.Thermal effect on quantum correlations of two interacting qubits in graphene latticeshttps://zbmath.org/1517.810232023-09-22T14:21:46.120933Z"Mhamdi, H."https://zbmath.org/authors/?q=ai:mhamdi.h"Jebli, L."https://zbmath.org/authors/?q=ai:jebli.larbi"Habiballah, N."https://zbmath.org/authors/?q=ai:habiballah.nabil"Nassik, M."https://zbmath.org/authors/?q=ai:nassik.mostafa(no abstract)Comparative dynamical study of a bound entangled statehttps://zbmath.org/1517.810242023-09-22T14:21:46.120933Z"Sinha, Suprabhat"https://zbmath.org/authors/?q=ai:sinha.suprabhatSummary: The bound entangled state carries noisy entanglement and it is very hard to distill but the usefulness of bound entangled states has been depicted in different applications. This article represents a comparative dynamical study of an open quantum system for one of the bound entangled states proposed by Bennett et al. The study is conducted under the influence of Heisenberg, bi-linear bi-quadratic and Dzyaloshinskii-Moriya (DM) interaction. During the study, an auxiliary qutrit interacts with one of the qutrits of the selected two qutrit bound entangled state through different interactions. The computable cross-norm or realignment (CCNR) criterion has been used to detect the bound entanglement of the state and the negativity has been applied to measure the free entanglement. From this three-fold study it is observed that, although the auxiliary qutrit plays a significant role during the interaction, the probability amplitude of the qutrit does not affect the open quantum system. Further, it is found that the Dzyaloshinskii-Moriya (DM) interaction performs better to activate the chosen bound entangled state among all the interactions.Entanglement entropy and non-local duality: quantum channels and quantum algebrashttps://zbmath.org/1517.810252023-09-22T14:21:46.120933Z"DeWolfe, Oliver"https://zbmath.org/authors/?q=ai:dewolfe.oliver"Higginbotham, Kenneth"https://zbmath.org/authors/?q=ai:higginbotham.kenneth-jSummary: We investigate the transformation of entanglement entropy under dualities, using the Kramers-Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality; instead, entangled states may be mapped to states with no local entanglement. To understand the fate of this entanglement, we consider two quantitative descriptions of degrees of freedom and their transformation under duality. The first involves Kraus operators implementing the partial trace as a quantum channel, while the second utilizes the algebraic approach to quantum mechanics, where degrees of freedom are encoded in subalgebras. Using both approaches, we show that entanglement of local degrees of freedom is not lost; instead it is transferred to non-local degrees of freedom by the duality transformation.Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systemshttps://zbmath.org/1517.810262023-09-22T14:21:46.120933Z"Lewenstein, Maciej"https://zbmath.org/authors/?q=ai:lewenstein.maciej"Müller-Rigat, Guillem"https://zbmath.org/authors/?q=ai:muller-rigat.guillem"Tura, Jordi"https://zbmath.org/authors/?q=ai:tura.jordi"Sanpera, Anna"https://zbmath.org/authors/?q=ai:sanpera.annaSummary: Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [\textit{M. Lewenstein} et al., Phys. Rev. A (3) 93, No. 4, Article ID 042335, 11 p. (2016; \url{doi:10.1103/PhysRevA.93.042335})], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an \(N\)-qubit system by proposing linear maps that, when applied to any state, result in a biseparable state for the \(1:(N-1)\) partitions, i.e., \((N-1)\)-entanglement depth. Furthermore, we derive criteria to detect arbitrary \((N-n)\)-entanglement depth tailored to states in close vicinity of the completely depolarized state (the normalized identity matrix). We also provide separability (or \(1\)-entanglement depth) conditions in the symmetric sector, including the diagonal states. Finally, we suggest how similar map techniques can be used to derive sufficient conditions for a set of expectation values to be compatible with separable states or local-hidden-variable theories. We dedicate this paper to the memory of the late Andrzej Kossakowski, our spiritual and intellectual mentor in the field of linear maps.Information-theoretical discord for a class of three-qubit X stateshttps://zbmath.org/1517.810272023-09-22T14:21:46.120933Z"Wei, Jia-Ning"https://zbmath.org/authors/?q=ai:wei.jianing"Duan, Zhou-Bo"https://zbmath.org/authors/?q=ai:duan.zhoubo"Zhang, Jun"https://zbmath.org/authors/?q=ai:zhang.jun.5Summary: Based on the definition of multipartite quantum discord proposed in [\textit{C. Radhakrishnan} et al., Phys. Rev. Lett. 124, No. 11, Article ID 110401, 6 p. (2020; \url{doi:10.1103/PhysRevLett.124.110401})], we give the analytic expression for the information-theoretical multipartite quantum discord of one type of three-qubit X states which depend on four real parameters. In addition, we present the level surfaces of multipartite quantum discord of X states. As an application, we investigate the dynamic behavior of multipartite quantum discord for the three-qubit X states under the phase flip channel, which presents the sudden change of multipartite quantum discord.Quantum conditional probabilities and new measures of quantum informationhttps://zbmath.org/1517.810282023-09-22T14:21:46.120933Z"Barandes, Jacob A."https://zbmath.org/authors/?q=ai:barandes.jacob-a"Kagan, David"https://zbmath.org/authors/?q=ai:kagan.davidSummary: We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von Neumann entropy. These quantities allow us to find new proofs of some standard results in quantum information theory, such as the concavity of von Neumann entropy and Holevo's theorem. The existence of an underlying probability distribution helps shed light on the conceptual underpinnings of these results.Criteria for SLOCC and LU equivalence of generic multi-qudit stateshttps://zbmath.org/1517.810292023-09-22T14:21:46.120933Z"Chang, Jingmei"https://zbmath.org/authors/?q=ai:chang.jingmei"Jing, Naihuan"https://zbmath.org/authors/?q=ai:jing.naihuan"Zhang, Tinggui"https://zbmath.org/authors/?q=ai:zhang.tingguiSummary: In this paper, we study the stochastic local operation and classical communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states by mode-\(n\) matricization of the coefficient tensors. We establish a new scheme of using the CANDECOMP/PARAFAC (CP) decomposition of tensors to find necessary and sufficient conditions between the mode-\(n\) unfolding and SLOCC\&LU equivalence for pure multi-qudit states. For multipartite mixed states, we present a necessary and sufficient condition for LU equivalence and necessary condition for SLOCC equivalence.Relativistic quantum thermometry through a moving sensorhttps://zbmath.org/1517.810302023-09-22T14:21:46.120933Z"Rangani Jahromi, Hossein"https://zbmath.org/authors/?q=ai:rangani-jahromi.hossein"Mamaghani, Samira Ebrahimi Asl"https://zbmath.org/authors/?q=ai:mamaghani.samira-ebrahimi-asl"Lo Franco, Rosario"https://zbmath.org/authors/?q=ai:lo-franco.rosarioSummary: Using a two-level moving probe, we address the temperature estimation of a static thermal bath modeled by a massless scalar field prepared in a thermal state. Different couplings of the probe to the field are discussed under various scenarios. We find that the thermometry is completely unaffected by the Lamb shift of the energy levels. We take into account the roles of probe velocity, its initial preparation, and environmental control parameters for achieving optimal temperature estimation. We show that a practical technique can be utilized to implement such a quantum thermometry. Finally, exploiting the thermal sensor moving at high velocity to probe temperature within a multiparameter-estimation strategy, we demonstrate perfect supremacy of the joint estimation over the individual one.Unidirectional information flow and positive divisibility are nonequivalent notions of quantum Markovianity for noninvertible dynamicshttps://zbmath.org/1517.810312023-09-22T14:21:46.120933Z"Rivas, Ángel"https://zbmath.org/authors/?q=ai:rivas.angelSummary: We construct a dynamical map which is not positive divisible and does not present information backflow either (as measured by trace norm quantifiers). It is formulated for a qutrit system undergoing noninvertible dynamics. This provides an evidence that the two definitions of quantum Markovianity based on the absence of information backflow and positive divisibility are nonequivalent for general noninvertible dynamical maps.Group of information differences in the extended parastatistics of quantum nonextensive systemshttps://zbmath.org/1517.810322023-09-22T14:21:46.120933Z"Zaripov, R. G."https://zbmath.org/authors/?q=ai:zaripov.rinat-g(no abstract)On quasi-inversion of quantum channels in 2 and in higher dimensionshttps://zbmath.org/1517.810332023-09-22T14:21:46.120933Z"Karimipour, Vahid"https://zbmath.org/authors/?q=ai:karimipour.vahidSummary: We review the concept of the quasi-inverse of qubit channels and of higher dimensional channels. Quasi-inverse is a channel which when concatenaded to the original channel, increases its average fidelity in an optimal way. For qubit channels, we fully characterize the quasi-inverse, while for higher dimensional channels, we prove general theorems and provide bounds for the increased average fidelity. Nevertheless, explicit examples are given when exact quasi-inverses can be found.Multi-proxy signature scheme using five-qubit entangled state based on controlled quantum teleportationhttps://zbmath.org/1517.810342023-09-22T14:21:46.120933Z"Fan, Ting-Ting"https://zbmath.org/authors/?q=ai:fan.tingting"Lu, Dian-Jun"https://zbmath.org/authors/?q=ai:lu.dianjun"You, Min-Guo"https://zbmath.org/authors/?q=ai:you.min-guo"Qian, Si-Jie"https://zbmath.org/authors/?q=ai:qian.si-jieSummary: With the upgrading of communication technology and the rapid development of quantum computing, the classical digital signature schemes are faced with unprecedented challenges, so the research on quantum digital signature is imperative. In this paper, we propose a multi-proxy signature scheme based on controlled quantum teleportation of five-qubit entangled state. In this scheme, quantum fourier transform is used as an encryption method to encrypt message, which improves the quantum efficiency compared with the quantum one-time pad. The five-qubit maximally entangled state which is qubit threshold quantum error correction required is used as the quantum channel to ensure the stability of the scheme. Security analysis shows that our scheme is unforgeable and undeniable, and it can resist the intercept-resend attack.The use of the output states generated by the broadcasting of entanglement in quantum teleportationhttps://zbmath.org/1517.810352023-09-22T14:21:46.120933Z"Ghiu, Iulia"https://zbmath.org/authors/?q=ai:ghiu.iulia"Cîrneci, Cătălina"https://zbmath.org/authors/?q=ai:cirneci.catalina"Nemneş, George Alexandru"https://zbmath.org/authors/?q=ai:nemnes.george-alexandruSummary: In this article, we find a theorem that gives a relation between the maximal fidelity of teleportation and the concurrence of the inseparable \(X\) state used as a quantum channel in this process. Furthermore, we evaluate the concurrence of the output states generated by the local and nonlocal asymmetric broadcasting of entanglement and prove that the concurrence is greater in the case of nonlocal broadcasting. We analyze the possibility of using the output states obtained by the broadcasting of entanglement as quantum channels in quantum teleportation. We prove, with the help of the above-mentioned theorem, that all the inseparable states given by the local and nonlocal asymmetric broadcasting of entanglement are useful for quantum teleportation. Finally, we show that the maximal fidelity of teleportation is greater in the case when the second scenario is used, i.e., when the quantum channel is generated by the nonlocal asymmetric broadcasting of entanglement.Probabilistic quantum teleportation via 3-qubit non-maximally entangled GHZ state by repeated generalized measurementshttps://zbmath.org/1517.810362023-09-22T14:21:46.120933Z"Javed, Shamiya"https://zbmath.org/authors/?q=ai:javed.shamiya"Pandey, Ravi Kamal"https://zbmath.org/authors/?q=ai:pandey.ravi-kamal"Yadav, Phool Singh"https://zbmath.org/authors/?q=ai:yadav.phool-singh"Prakash, Ranjana"https://zbmath.org/authors/?q=ai:prakash.ranjana"Prakash, Hari"https://zbmath.org/authors/?q=ai:prakash.hariSummary: We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of \(\sigma_x\). Both these measurement outcomes are communicated to Bob classically, which helps him to perform a suitable unitary transformation on qubit 3 to recover the information state. On the other hand, if failure is obtained, the next attempt of GBSM is performed on qubits 0 and 2. This process of repeating GBSM on alternate pair of qubits may continue until perfect teleportation with unit fidelity is achieved. We have obtained analytical expressions for success probability up to three repetitions of GBSM. The success probability is shown to be a polynomial function of bipartite concurrence of the NME resource. The variation of success probability with the bipartite concurrence has been plotted which shows the convergence of success probability to unity with GBSM repetitions.Ray-marching Thurston geometrieshttps://zbmath.org/1517.810372023-09-22T14:21:46.120933Z"Coulon, Rémi"https://zbmath.org/authors/?q=ai:coulon.remi"Matsumoto, Elisabetta A."https://zbmath.org/authors/?q=ai:matsumoto.elisabetta-a"Segerman, Henry"https://zbmath.org/authors/?q=ai:segerman.henry"Trettel, Steve J."https://zbmath.org/authors/?q=ai:trettel.steve-jSummary: We describe algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching. We give a theoretical framework for our algorithms, independent of the geometry involved. In addition to scenes within a geometry \(X\), we also consider scenes within quotient manifolds and orbifolds \(X / \Gamma\). We adapt the Phong lighting model to non-Euclidean geometries. The most difficult part of this is the calculation of light intensity, which relates to the area density of geodesic spheres. We also give extensive practical details for each geometry.Discontinuous Galerkin method with Voronoi partitioning for quantum simulation of chemistryhttps://zbmath.org/1517.810382023-09-22T14:21:46.120933Z"Faulstich, Fabian M."https://zbmath.org/authors/?q=ai:faulstich.fabian-m"Wu, Xiaojie"https://zbmath.org/authors/?q=ai:wu.xiaojie"Lin, Lin"https://zbmath.org/authors/?q=ai:lin.linSummary: To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) basis set with a rectangular partitioning strategy was recently introduced [\textit{J. R. McClean} et al, New J. Phys. 22, No. 9, Article ID 093015, 25 p. (2020; \url{doi:10.1088/1367-2630/ab9d9f})]. We propose and numerically scrutinize a more general DG basis set construction based on a Voronoi decomposition with respect to the nuclear coordinates. This allows the construction of DG basis sets for arbitrary molecular and crystalline configurations. We here employ the planewave dual basis set as primitive basis set in the supercell model; as a set of grid-based nascent delta functions, the planewave dual functions provide sufficient flexibility for the Voronoi partitioning. The presented implementation of this \textit{DG-Voronoi} approach is in Python and solely based on PySCF. We numerically investigate the performance, at the mean-field and correlated level of theory for quasi-1D, quasi-2D and fully 3D systems, and exemplify the application to crystalline systems.Entangled state engineering in the 4-coupled qubits systemhttps://zbmath.org/1517.810392023-09-22T14:21:46.120933Z"Salmanogli, Ahmad"https://zbmath.org/authors/?q=ai:salmanogli.ahmadSummary: This article studies the behavior of the avoided level crossing in the 4-coupled qubit to each other and mainly focuses on how to engineer it. This phenomenon occurs due to the two transitions out of the ground state in a two-coupled qubit, contributing to the entangled states. This essential and unique behavior can be engineered in a quantum circuit. For this reason, a quantum circuit containing 4 qubits is designed, and its quantum Hamiltonian and dynamic equation of the motion are theoretically derived. Analysis of the entanglement between each coupled qubit using the entanglement metric reveals that the strength of the qubit-qubit coupling factor and the qubit's non-linearity play an essential role in engineering the photonic mode entanglement. The results show that the avoided level crossing appears in the photonic mode entanglement. In other words, two or more transitions from the ground state to the multiple excited states for each bias current. However, the interesting point is that the avoided level crossing just occurs for the qubits connected capacitively to the driven field (the first qubit in this work), not for all.Statistical properties of non-Gaussian quantum states generated via thermal state truncationhttps://zbmath.org/1517.810402023-09-22T14:21:46.120933Z"Wang, Lei"https://zbmath.org/authors/?q=ai:wang.lei.206"Wang, Ji-Suo"https://zbmath.org/authors/?q=ai:wang.jisuo"Zhang, Xiao-Yan"https://zbmath.org/authors/?q=ai:zhang.xiaoyan.2"Meng, Xiang-Guo"https://zbmath.org/authors/?q=ai:meng.xiangguo"Yu, Zhao-Xian"https://zbmath.org/authors/?q=ai:yu.zhaoxianSummary: Quantum scissors devices proposed by Pegg are beneficial to obtain highly nonclassical quantum states and indispensable for meeting the requirements of quantum information and computation. In this paper, via inputting and detecting single photon states, quantum scissor operation is equivalent to a mixed superposition of three pure state projection operators, which means that the output states are always truncated for any input state. We theoretically prepare a class of non-Gaussian quantum states via thermal state truncation and investigate their statistical properties using average photon number, gain intensity and signal to noise ratio. It is shown that the intensity gain and signal to noise ratio greater than one can be achieved by modulating the thermal parameter and the transmissivity, which realizes the signal amplification and enhancement. Besides, quantum scissor operation can generate the highly non-classical quantum state by investigating the negativity volume of Wigner function. These results indicate that the usage of the new non-Gaussian states may have potential applications in certain quantum information processing.A tree-type multiparty quantum key agreement protocol against collusive attackshttps://zbmath.org/1517.810412023-09-22T14:21:46.120933Z"Yang, Hao"https://zbmath.org/authors/?q=ai:yang.hao.2"Lu, Songfeng"https://zbmath.org/authors/?q=ai:lu.songfeng"Zhu, Jianxin"https://zbmath.org/authors/?q=ai:zhu.jianxin"Wu, Junjun"https://zbmath.org/authors/?q=ai:wu.junjun"Zhou, Qing"https://zbmath.org/authors/?q=ai:zhou.qing"Li, Tong"https://zbmath.org/authors/?q=ai:li.tong|li.tong.1Summary: Multiparty quantum key agreement (MQKA) requires sharing a secure and fair key among participants. However, several malicious participants may collude together to steal the privacy of honest participants or determine the shared key, privately. In this work, we propose a tree-type MQKA protocol against collusive attacks, in which the entanglement swapping technology of multi-particle entangled states is used to construct the shared key. Compared with the previous MQKA protocols against collusive attacks, our scheme consumes fewer qubits and only needs to transmit quantum states once, which significantly reduces the consumption of quantum resources.The intrinsic decoherence effects on nonclassical correlations in a dipole-dipole two-spin system with Dzyaloshinsky-Moriya interactionhttps://zbmath.org/1517.810422023-09-22T14:21:46.120933Z"Oumennana, Mansoura"https://zbmath.org/authors/?q=ai:oumennana.mansoura"Chaouki, Essalha"https://zbmath.org/authors/?q=ai:chaouki.essalha"Mansour, Mostafa"https://zbmath.org/authors/?q=ai:mansour.mostafaSummary: Bipolar spin systems are expected to provide a reliable and scalable platform for advances in quantum computing and nanotechnology. Thus, the survey of the dynamics of the quantum properties of such systems is of paramount importance. This work explores the dynamics of bipartite entanglement and nonclassical correlations in a dipole-dipole two spin system with Dzyaloshinsky-Moriya (DM) interaction and under the influence of the intrinsic decoherence effects. We employ logarithmic negativity to quantify quantum entanglement. Local quantum uncertainty and quantum discord are employed to capture non-classical correlations beyond entanglement in the considered system. For this purpose, we consider that the system is initially prepared in a Werner state and we explore the effect of intrinsic decoherence rate, dipolar coupling parameters between the spins, strength of the Dzyaloshinsky-Moriya interaction and the intensities of the homogeneous magnetic fields on the dynamics of the three quantifiers of correlations within the considered system. The findings reveal that intrinsic decoherence deteriorates quantum correlations, while the dipolar coupling constant diminishes the oscillatory behavior observed but enhances the robustness of bipartite entanglement and nonclassical correlations. The negative effects of the intrinsic decoherence on the quantum correlations can be mitigated by adjusting the values of the system's parameters as well as the Dzyaloshinsky-Moriya coupling parameter. We also show that the three studied measures behave quasi-similarly. Finally, we depict that the amounts of entanglement and nonclassical correlations within the system are closely tied to the system's degree of purity.Quantum private magnitude comparison based on maximum operationhttps://zbmath.org/1517.810432023-09-22T14:21:46.120933Z"Zhou, Lin-tao"https://zbmath.org/authors/?q=ai:zhou.lintao"Lang, Yan-Feng"https://zbmath.org/authors/?q=ai:lang.yan-feng"Zhao, Zi-Hao"https://zbmath.org/authors/?q=ai:zhao.zihaoSummary: Many existed quantum private comparison (QPC) protocols can determine whether two secrets are equal or not, while the quantum private magnitude comparison (QPMC) protocol by Lang can output three results: greater than, equal and less than for two private data. In order to implement the magnitude comparison, it defined the minimum operation. However, if we only rely on this operation to implement QPMC, it may not be efficient at cooperating with some quantum resources. For this reason, it is necessary for us to introduce another operation -- maximum one. With regard to some quantum resources, only by using the maximum operation are we able to realize a simple and efficient QPMC. In this paper, it is the maximum operation that helps us utilize a single Bell state to propose a QPMC protocol in an easy and efficient way. The protocol is fully analysed for its correctness and security. The analyses prove that the presented protocol is not only simple yet efficient but also of low costs. It would be a better alternative for QPMC.Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivationshttps://zbmath.org/1517.810442023-09-22T14:21:46.120933Z"Bagarello, F."https://zbmath.org/authors/?q=ai:bagarello.fabioSummary: In some recent literature the role of non self-adjoint Hamiltonians, \(H\neq H^\dagger\), is often considered in connection with gain-loss systems. The dynamics for these systems is, most of the times, given in terms of a Schrödinger equation. In this paper we rather focus on the Heisenberg-like picture of quantum mechanics, stressing the (few) similarities and the (many) differences with respected to the standard Heisenberg picture for systems driven by self-adjoint Hamiltonians. In particular, the role of the symmetries, \(\ast\)-derivations and integrals of motion is discussed.On the stationary non-equilibrium measures for the ``field-crystal'' systemhttps://zbmath.org/1517.810452023-09-22T14:21:46.120933Z"Dudnikova, T. V."https://zbmath.org/authors/?q=ai:dudnikova.tatyana-vSummary: In the paper, we consider the Cauchy problem for a Hamiltonian system consisting of a Klein-Gordon field and an infinite harmonic crystal. We assume that the initial data of the problem are a random function and study the convergence of the distributions of the solutions to a limiting measure for large times. Under the condition that the initial random function in the ``left'' and ``right'' parts of the space has the Gibbs distribution with different temperatures, we find the stationary states of the system in which the limiting energy current density does not vanish. Thus, for this system, a class of stationary non-equilibrium states is constructed.Stability of the classical catenoid and Darboux-Pöschl-Teller potentialshttps://zbmath.org/1517.810462023-09-22T14:21:46.120933Z"Hoppe, Jens"https://zbmath.org/authors/?q=ai:hoppe.jens"Moosavi, Per"https://zbmath.org/authors/?q=ai:moosavi.perSummary: We revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable one-dimensional Schrödinger operator with an asymmetric Darboux-Pöschl-Teller potential.Critical points at infinity in charged \(N\)-body systemshttps://zbmath.org/1517.810472023-09-22T14:21:46.120933Z"Hoveijn, I."https://zbmath.org/authors/?q=ai:hoveijn.igor"Waalkens, H."https://zbmath.org/authors/?q=ai:waalkens.holger"Zaman, M."https://zbmath.org/authors/?q=ai:zaman.musharaff|zaman.mashiyat|zaman.mehwish|zaman.mirSummary: We define the notion of critical points at infinity for the charged \(N\)-body problem, following the approach of \textit{A. Albouy} [Invent. Math. 114, No. 3, 463--488 (1993; Zbl 0801.70008)]. We give a characterisation of such points and show how they can be found in the charged 3-body problem. The symmetry group of the \(N\)-body problem and accompanying integrals play a key role. In fact critical points at infinity are indispensible in understanding the bifurcations of the integral map. Together with the critical points at infinity in the charged 3-body problem, we present the bifurcation values.Complexity is a matter of distancehttps://zbmath.org/1517.810482023-09-22T14:21:46.120933Z"Javarone, Marco Alberto"https://zbmath.org/authors/?q=ai:javarone.marco-albertoSummary: Complex systems constitute a cross-disciplinary field that studies natural and societal phenomena. In general, complexity relates to different aspects of a system, such as emergent behaviours, interaction patterns, and other properties. Also, complexity can refer to the resources required to accomplish a task. Here, we review a limited collection of methods for studying complexity across different topics. The resulting picture highlights interesting relationships between complexity and distance, showing up in all considered systems, from phase transitions to black hole evolution. We conclude by discussing related implications and a few examples beyond Physics that corroborate the validity of the highlighted relationships.Superintegrability summaryhttps://zbmath.org/1517.810492023-09-22T14:21:46.120933Z"Mironov, A."https://zbmath.org/authors/?q=ai:mironov.a-v|mironov.a-p|mironov.a-b|mironov.andrei-d|mironov.artem-sergeevich|mironov.a-g|mironov.a-k|mironov.andrei-evgenevich|mironov.andrew-m|mironov.aleksei-nikolaevich|mironov.a-a|mironov.a-l"Morozov, A."https://zbmath.org/authors/?q=ai:morozov.anatolii-nikolaevich|morozov.a-v|morozov.alexander-yu|morozov.andrei-igorevich|morozov.a-g|morozov.andrew-yu|morozov.alexei-yurievich|morozov.alexandre-v|morozov.alexander-n|morozov.a-a|morozov.andrey-n|morozov.a-m|morozov.a-k|morozov.anton|morozov.albert-dmitrievich|morozov.a-c|morozov.andrei-sergeevich|morozov.andrei-alekseevichSummary: We enumerate generalizations of the superintegrability property \(<\) \textit{character} \(>\) \(\sim\) character and illuminate possible general structures behind them. We collect variations of original formulas available up to date, and emphasize the remaining difference between the cases of Hermitian and complex matrices, bosonic and fermionic ones. Especially important is that the story is in no way restricted to Gaussian potentials.On the statistical generator of solutions to the Schrödinger equationhttps://zbmath.org/1517.810502023-09-22T14:21:46.120933Z"Plokhotnikov, K. È."https://zbmath.org/authors/?q=ai:plokhotnikov.k-ehSummary: The article describes the procedure for generating solutions to the Schrödinger equation by the Monte Carlo method. As a demonstration quantum system illustrating this generator, clusters of water: hexamer \(6(\mathrm{H}_2\mathrm{O})\), dodecamer \(12(\mathrm{H}_2\mathrm{O})\) and tetradecamer \(14(\mathrm{H}_2\mathrm{O})\) act. The generator of solutions to the Schrödinger equations is derived from the algorithm proposed by the author earlier, based on the intersection of the finite-difference and Monte Carlo approaches, as well as methods of spatial reduction of scattering centers of particle nuclei and scattering centers of electrons of an arbitrary quantum system, tested on water clusters. As a result of this information, it turned out to be possible to construct an algorithm for generating an unlimited number of different spatial structures of scattering clouds of particle nuclei and electrons at the same dissociation energy of a quantum system.On expansions in the exact and asymptotic eigenfunctions of the one-dimensional Schrödinger operatorhttps://zbmath.org/1517.810512023-09-22T14:21:46.120933Z"Anikin, A. Yu."https://zbmath.org/authors/?q=ai:anikin.a-yu"Dobrokhotov, S. Yu."https://zbmath.org/authors/?q=ai:dobrokhotov.sergei-yu"Shkalikov, A. A."https://zbmath.org/authors/?q=ai:shkalikov.andrei-andreevichSummary: The one-dimensional Schrödinger operator with potential growing at infinity and with a semiclassical small parameter is considered. We obtain estimates via powers of the small parameter for the remainder in the expansion of smooth sufficiently rapidly decaying functions in the exact and asymptotic eigenfunctions. For the asymptotic eigenfunctions, we use a global representation in the form of an Airy function.Riesz potential for \((k,1)\)-generalized Fourier transformhttps://zbmath.org/1517.810522023-09-22T14:21:46.120933Z"Ivanov, Valeriĭ Ivanovich"https://zbmath.org/authors/?q=ai:ivanov.valerii-ivanovichSummary: In spaces with weight \(|x|^{-1}v_k(x)\), where \(v_k(x)\) is the Dunkl weight, there is the \((k,1)\)-generalized Fourier transform. Harmonic analysis in these spaces is important, in particular, in problems of quantum mechanics. We define the Riesz potential for the \((k,1)\)-generalized Fourier transform and prove for it, a \((L^q,L^p)\)-inequality with radial power weights, which is an analogue of the well-known Stein-Weiss inequality for the classical Riesz potential. For the Riesz potential we calculate the sharp value of the \(L^p\)-norm with radial power weights. The sharp value of the \(L^p\)-norm with radial power weights for the classical Riesz potential was obtained independently by W. Beckner and S. Samko.Reply to: ``Comment on: `On the characteristic polynomial of an effective Hamiltonian{'}''https://zbmath.org/1517.810532023-09-22T14:21:46.120933Z"Zheng, Yong"https://zbmath.org/authors/?q=ai:zheng.yongSummary: In a recent comment by \textit{F. M. Fernández} [Phys. Lett., A 452, Article ID 128456, 3 p. (2022; Zbl 1515.81103)], it has been argued that our solution method of an effective Hamiltonian based on the characteristic polynomial [the author, Phys. Lett., A 443, Article ID 128215, 5 p. (2022; Zbl 1498.81077)] had been developed several years earlier by \textit{L. E. Fried} and \textit{G. S. Ezra} [J. Chem. Phys. 90, 6378--6390 (1989; \url{doi:10.1063/1.456303})]. We show here several important differences between our treatment and the resummation method proposed previously by Fried and Ezra.Systematics of quasi-Hermitian representations of non-Hermitian quantum modelshttps://zbmath.org/1517.810542023-09-22T14:21:46.120933Z"Znojil, Miloslav"https://zbmath.org/authors/?q=ai:znojil.miloslavSummary: In the currently quickly growing area of applications of non-Hermitian Hamiltonians \(H\neq H^\dagger\) which are quasi-Hermitian (i.e., such that \(H^\dagger\Theta=\Theta H\), with a suitable inner-product metric \(\Theta\neq I)\), the correct probabilistic interpretation of the model is needed. Achieved either in the Buslaev-Grecchi-inspired spirit (BGI; one factorizes \(\Theta=\Omega^\dagger\Omega\) and reconstructs the conventional Hermitian Hamiltonian, \(H\to \mathfrak{h}=\Omega H\Omega^{-1}=\mathfrak{h}^\dagger)\) or in the much user-friendlier, Dyson-inspired spirit (DI; one eliminates the ``difficult'' reference to \(\mathfrak{h}\) via the quasi-Hermiticity rule, i.e., via an ``easier'' reconstruction of \(\Theta)\). Here, the two model-building BGI and DI recipes are identified as the two extreme special cases of a general correct-interpretation-providing strategy. We show that at any preselected integer \(N\) one may make a choice between the BGI extreme and an \(N\)-plet of the other, consistent and physical DI-type representations of the system in which a specific, partially modified Hamiltonian is constructed as quasi-Hermitian with respect to a specific, simplified inner-product metric. In applications, any one of these \(N+1\) options may prove optimal for a given \(H\): A schematic three-state quantum system is discussed as an illustrative example.Universality near the gradient catastrophe point in the semiclassical sine-Gordon equationhttps://zbmath.org/1517.810552023-09-22T14:21:46.120933Z"Lu, Bing-Ying"https://zbmath.org/authors/?q=ai:lu.bing-ying"Miller, Peter"https://zbmath.org/authors/?q=ai:miller.peter-dSummary: We study the semiclassical limit of the sine-Gordon (sG) equation with below threshold pure impulse initial data of Klaus-Shaw type. The Whitham averaged approximation of this system exhibits a gradient catastrophe in finite time. In accordance with a conjecture of \textit{B. Dubrovin} et al. [J. Nonlinear Sci. 19, No. 1, 57--94 (2009; Zbl 1220.37048)], we found that in a \(\mathcal{O}(\epsilon^{4/5})\) neighborhood near the gradient catastrophe point, the asymptotics of the sG solution are universally described by the Painlevé I tritronquée solution. A linear map can be explicitly made from the tritronquée solution to this neighborhood. Under this map: away from the tritronquée poles, the first correction of sG is universally given by the real part of the Hamiltonian of the tritronquée solution; localized defects appear at locations mapped from the poles of the tritronquée solution; the defects are proved universally to be a two-parameter family of special localized solutions on a periodic background for the sG equation. We are able to characterize the solution in detail. Our approach is the rigorous steepest descent method for matrix Riemann-Hilbert problems, substantially generalizing [5] to establish universality beyond the context of solutions of a single equation.Semiclassical asymptotics of oscillating tunneling for a quadratic Hamiltonian on the algebra \(\operatorname{su}(1,1)\)https://zbmath.org/1517.810562023-09-22T14:21:46.120933Z"Vybornyi, E. V."https://zbmath.org/authors/?q=ai:vybornyi.e-v"Rumyantseva, S. V."https://zbmath.org/authors/?q=ai:rumyantseva.s-vSummary: In this paper, we consider the problem of constructing semiclassical asymptotics for the tunnel splitting of the spectrum of an operator defined on an irreducible representation of the Lie algebra \(\operatorname{su}(1,1)\). It is assumed that the operator is a quadratic function of the generators of the algebra. We present coherent states and a unitary coherent transform that allow us to reduce the problem to the analysis of a second-order differential operator in the space of holomorphic functions. Semiclassical asymptotic spectral series and the corresponding wave functions are constructed as decompositions in coherent states. For some values of the system parameters, the minimal energy corresponds to a pair of nondegenerate equilibria, and the discrete spectrum of the operator has an exponentially small tunnel splitting of the levels. We apply the complex WKB method to prove asymptotic formulas for the tunnel splitting of the energies. We also show that, in contrast to the one-dimensional Schrödinger operator, the tunnel splitting in this problem not only decays exponentially but also contains an oscillating factor, which can be interpreted as tunneling interference between distinct instantons. We also show that, for some parameter values, the tunneling is completely suppressed and some of the spectral levels are doubly degenerate, which is not typical of one-dimensional systems.Fermionic contribution to the anomalous dimension of twist-2 operators in \(\mathcal{N} = 4\) SYM theory, critical indices and integrabilityhttps://zbmath.org/1517.810572023-09-22T14:21:46.120933Z"Velizhanin, V. N."https://zbmath.org/authors/?q=ai:velizhanin.v-nSummary: We compute the contribution to the anomalous dimension of the twist-2 operators in \(\mathcal{N} = 4\) SYM theory, which is proportional to the number of fermion loops inside Feynman diagrams or, formally, to the number of fermions. The result was obtained by the method based on the calculation of critical indices at the critical point by analogy with previous similar computations in scalar theories and in QCD. The obtained result is much simpler with compare to analogous results in QCD and almost satisfies the maximal transcendentality principle. A possible relation between the obtained result and integrability is discussed.Emergent time crystals from phase-space noncommutative quantum mechanicshttps://zbmath.org/1517.810582023-09-22T14:21:46.120933Z"Bernardini, A. E."https://zbmath.org/authors/?q=ai:bernardini.alex-e"Bertolami, O."https://zbmath.org/authors/?q=ai:bertolami.orfeuSummary: It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our point is that such effects do emerge from position (\(\hat{q}_i\)) and/or momentum (\(\hat{p}_i\)) noncommutativity, i.e., from \([\hat{q}_i, \hat{q}_j] \neq 0\) and/or \([\hat{p}_i, \hat{p}_j] \neq 0\) (for \(i \neq j\)). In such a context, a predictive analysis is carried out for the 2-dim noncommutative quantum harmonic oscillator through a procedure supported by the Weyl-Wigner-Groenewold-Moyal framework. This allows for the understanding of how the phase-space noncommutativity drives the amplitude of periodic oscillations identified as time crystals. A natural extension of our analysis also shows how the spontaneous formation of time quasi-crystals can arise.Band structure of the one-dimensional spin-orbit-coupled Su-Schrieffer-Heeger lattice with \(\mathcal{PT}\)-symmetric onsite imaginary potentialshttps://zbmath.org/1517.810592023-09-22T14:21:46.120933Z"Li, Jia-Rui"https://zbmath.org/authors/?q=ai:li.jiarui"Wang, Zi-An"https://zbmath.org/authors/?q=ai:wang.zian"Zhang, Lian-Lian"https://zbmath.org/authors/?q=ai:zhang.lian-lianSummary: Energy band structures of one-dimensional non-Hermitian spin-orbit-coupled Su-Schrieffer-Heeger (SSH) model are theoretically investigated, by introducing imaginary potentials with gain and loss effects. It is found that the imaginary potentials can promote the occurrence of \(\mathcal{PT}\)-symmetry breaking. In the topologically-nontrivial regions, the different imaginary parts of the edge-state energies leads to the different localization degrees of such states. Moreover, gapless phase regions arise between the topologically-nontrivial and -trivial regions, in which edge states are allowed to survive. Therefore, these results are helpful to understand the band-structural and topological properties of \(\mathcal{PT}\)-symmetric non-Hermitian systems.Lattice fermionic Casimir effect in a slab bag and universalityhttps://zbmath.org/1517.810602023-09-22T14:21:46.120933Z"Mandlecha, Yash V."https://zbmath.org/authors/?q=ai:mandlecha.yash-v"Gavai, Rajiv V."https://zbmath.org/authors/?q=ai:gavai.rajiv-vSummary: We apply the physically more appealing MIT Bag boundary conditions to study the Casimir effect on the lattice. Employing the formalism of [\textit{T. Ishikawa} et al., Phys. Lett., B 809, Article ID 135713, 7 p. (2020; Zbl 1473.81170)] to calculate the Casimir energy for free lattice fermions, we show that the results for the naive, Wilson and overlap fermions match the continuum expressions precisely in the zero lattice spacing limit, as expected from universality. In contrast to [loc. cit.] where the result for the naive fermions rapidly oscillates with the lattice size for both, the periodic (P) and antiperiodic (AP) boundary conditions, no oscillations are observed with the lattice size. Furthermore, the apparent violation of the universality for naive fermion in [loc. cit.] is shown to be cured by applying suitable series extrapolation techniques, thus demonstrating that the Casimir energy for the naive fermions with periodic/antiperiodic boundary conditions agrees with the results for other free lattice fermions, and can be used to obtain the results for the Dirac fermion in the zero limit of the lattice spacing.Semiclassical calculation of time delay statistics in chaotic quantum scatteringhttps://zbmath.org/1517.810612023-09-22T14:21:46.120933Z"Novaes, Marcel"https://zbmath.org/authors/?q=ai:novaes.marcelSummary: We present a semiclassical calculation, based on classical action correlations implemented by means of a matrix integral, of all moments of the Wigner-Smith time delay matrix, \(Q\), in the context of quantum scattering through systems with chaotic dynamics. Our results are valid for broken time reversal symmetry and depend only on the classical dwell time and the number of open channels, \(M\), which is arbitrary. Agreement with corresponding random matrix theory reduces to an identity involving some combinatorial concepts, which can be proved in special cases.Almost contact structures on manifolds with a \(G_2\) structurehttps://zbmath.org/1517.810622023-09-22T14:21:46.120933Z"de la Ossa, Xenia"https://zbmath.org/authors/?q=ai:ossa.xenia-de-la"Larfors, Magdalena"https://zbmath.org/authors/?q=ai:larfors.magdalena"Magill, Matthew"https://zbmath.org/authors/?q=ai:magill.matthewSummary: We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a \(G_2\) structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the \(SU(3)\) structure associated to an ACMS and apply these computations to heterotic \(G_2\) systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.A group theoretic description of the \(\kappa\)-Poincaré Hopf algebrahttps://zbmath.org/1517.810632023-09-22T14:21:46.120933Z"Arzano, Michele"https://zbmath.org/authors/?q=ai:arzano.michele"Kowalski-Glikman, Jerzy"https://zbmath.org/authors/?q=ai:kowalski-glikman.jerzySummary: It is well known in the literature that the momentum space associated to the \(\kappa\)-Poincaré algebra is described by the Lie group \(\mathsf{AN}(3)\). In this letter we show that the full \(\kappa\)-Poincaré Hopf algebra structure can be obtained from rather straightforward group-theoretic manipulations starting from the Iwasawa decomposition of the \(\mathsf{SO}(1, 4)\) group.A Landau-Ginzburg mirror theorem via matrix factorizationshttps://zbmath.org/1517.810642023-09-22T14:21:46.120933Z"He, Weiqiang"https://zbmath.org/authors/?q=ai:he.weiqiang"Polishchuk, Alexander"https://zbmath.org/authors/?q=ai:polishchuk.alexander-e"Shen, Yefeng"https://zbmath.org/authors/?q=ai:shen.yefeng"Vaintrob, Arkady"https://zbmath.org/authors/?q=ai:vaintrob.arkadySummary: For an invertible quasihomogeneous polynomial \(\boldsymbol{w}\) we prove an all-genus mirror theorem relating two cohomological field theories of Landau-Ginzburg type. On the \(B\)-side it is the Saito-Givental theory for a specific choice of a primitive form. On the \(A\)-side, it is the matrix factorization CohFT for the dual singularity \(\boldsymbol{w}^T\) with the maximal diagonal symmetry group.Covariant holographic reflected entropy in \(AdS_3/CFT_2\)https://zbmath.org/1517.810652023-09-22T14:21:46.120933Z"Afrasiar, Mir"https://zbmath.org/authors/?q=ai:afrasiar.mir"Chourasiya, Himanshu"https://zbmath.org/authors/?q=ai:chourasiya.himanshu"Raj, Vinayak"https://zbmath.org/authors/?q=ai:raj.vinayak"Sengupta, Gautam"https://zbmath.org/authors/?q=ai:sengupta.gautamSummary: We substantiate a covariant proposal for the holographic reflected entropy in \(CFT\)s dual to non-static \(AdS\) geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the \(AdS_3/CFT_2\) scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in \(CFT_{1 + 1}\)s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for these bulk geometries in the literature. This constitutes a significant consistency check for the proposal and its possible extension to the corresponding higher dimensional \(AdS/CFT\) scenario.A consistent description of the relativistic effects and three-body interactions in atomic nucleihttps://zbmath.org/1517.810662023-09-22T14:21:46.120933Z"Yang, Y. L."https://zbmath.org/authors/?q=ai:yang.yunlei|yang.yulin|yang.yueli|yang.yalin|yang.yunlong.1|yang.yanli|yang.yaling|yang.yongliang|yang.yuliang|yang.yueling|yang.youlong|yang.yilong|yang.yinlong|yang.yuli|yang.yilu|yang.yanlong|yang.yuling|yang.yulu|yang.yunli|yang.yeong-ling|yang.yunle|yang.yong-li|yang.yulong|yang.yilin|yang.young-lyeol|yang.ya-lan|yang.yung-lieh|yang.yiling|yang.yanling|yang.yali|yang.yonglin"Zhao, P. W."https://zbmath.org/authors/?q=ai:zhao.peiwu|zhao.pengweiSummary: A microscopic relativistic Hamiltonian containing consistent relativistic and \(3N\) potentials is, for the first time, constructed based on the leading-order covariant pionless effective field theory, and this Hamiltonian is solved by developing a new accurate relativistic \textit{ab initio} method with a novel symmetry-based artificial neural network for \(A \leq 4\) nuclei. It is found that the relativistic effects overcome the energy collapse problem for \(^3\mathrm{H}\) and \(^4\mathrm{He}\) without promoting a repulsive three-nucleon interaction to leading order as in nonrelativistic calculations. To exactly reproduce the experimental ground-state energies, a three-nucleon interaction is needed and its interplay with the relativistic effects plays a crucial role. The presented results open the new avenue for a unified and consistent study on relativistic effects and many-body interactions in atomic nuclei, and would also help to achieve more accurate \textit{ab initio} calculations for nuclei.Dirac series of \(E_{7 (- 5)}\)https://zbmath.org/1517.810672023-09-22T14:21:46.120933Z"Ding, Yi-Hao"https://zbmath.org/authors/?q=ai:ding.yihao"Dong, Chao-Ping"https://zbmath.org/authors/?q=ai:dong.chao-ping"Li, Ping-Yuan"https://zbmath.org/authors/?q=ai:li.pingyuanSummary: Using the sharpened Helgason-Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of \(E_{7 (- 5)}\). As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of \(E_{7 (- 5)}\). Assuming the infinitesimal character being integral, we further improve the Helgason-Johnson bound for \(E_{7 (- 5)}\). This should help people to understand (part of) the unitary dual of this group.Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by \(XX\)-Hamiltonianhttps://zbmath.org/1517.810682023-09-22T14:21:46.120933Z"Fel'dman, E. B."https://zbmath.org/authors/?q=ai:feldman.eduard-b"Zenchuk, A. I."https://zbmath.org/authors/?q=ai:zenchuk.alexandre-iSummary: The approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) when the intensity of spin-spin interaction is \(\sim 1/r^3\), where \(r\) is a distance between those spins. However, NNI can not approximate the long time evolution in such systems. We consider the system with the intensity of the spin-spin interaction \(\sim 1/r^\alpha\), \(\alpha\geq3\), and find the low boundary \(\alpha_c\) of applicability of the NNI to the evolution of an arbitrary one-excitation initial quantum state in the homogeneous spin chain governed by the \(XX\)-Hamiltonian. We obtain the logarithmic dependence of \(\alpha_c\) on the chain length.Twisted composition algebras and Arthur packets for triality Spin\(_8\)https://zbmath.org/1517.810692023-09-22T14:21:46.120933Z"Gan, Wee Teck"https://zbmath.org/authors/?q=ai:gan.wee-teck"Savin, Gordan"https://zbmath.org/authors/?q=ai:savin.gordanSummary: The purpose of this paper is to construct and analyze certain square-integrable automorphic forms on the quasi-split simply-connected groups \(\mathrm{Spin}_8\) of type \(D_4\) over a number field \(F\). Since the outer automorphism group of \(\mathrm{Spin}_8\) is \(S_3\), these quasi-split groups are parametrised by étale cubic \(F\)-algebras \(E\) and we denote them by \(\mathrm{Spin}^E_8\) (to indicate the dependence on \(E)\). We shall specialize to the case when \(E\) is a cubic field: this gives the so-called triality \(\mathrm{Spin}_8\).Random walk on quantum blobshttps://zbmath.org/1517.810702023-09-22T14:21:46.120933Z"Jadczyk, Arkadiusz"https://zbmath.org/authors/?q=ai:jadczyk.arkadiuszSummary: We describe the action of the symplectic group on the homogeneous space of squeezed states (quantum blobs) and extend this action to the semigroup. We then extend the metaplectic representation to the metaplectic (or oscillator) semigroup and study the properties of such an extension using Bargmann-Fock space. The shape geometry of squeezing is analyzed and noncommuting elements from the symplectic semigroup are proposed to be used in simultaneous monitoring of noncommuting quantum variables -- which should lead to fractal patterns on the manifold of squeezed states.Noncommutative tensor triangular geometryhttps://zbmath.org/1517.810712023-09-22T14:21:46.120933Z"Nakano, Daniel K."https://zbmath.org/authors/?q=ai:nakano.daniel-k"Vashaw, Kent B."https://zbmath.org/authors/?q=ai:vashaw.kent-b"Yakimov, Milen T."https://zbmath.org/authors/?q=ai:yakimov.milen-tSummary: We develop a general noncommutative version of s tensor triangular geometry that is applicable to arbitrary monoidal triangulated categories M\(\Delta\)Cs). Insight from noncommutative ring theory is used to obtain a framework for prime, semiprime, and completely prime (thick) ideals of an M\(\Delta\)C, \textbf{K}, and then to associate to \textbf{K} a topological space-the Balmer spectrum \(\operatorname{Spc} \mathbf{K}\). We develop a general framework for (noncommutative) support data, coming in three different flavors, and show that \(\operatorname{Spc} \mathbf{K}\) is a universal terminal object for the first two notions (support and weak support). The first two types of support data are then used in a theorem that gives a method for the explicit classification of the thick (two-sided) ideals and the Balmer spectrum of an M\(\Delta\)C. The third type (quasi support) is used in another theorem that provides a method for the explicit classification of the thick right ideals of \textbf{K}, which in turn can be applied to classify the thick two-sided ideals and \(\operatorname{Spc} \mathbf{K}\).
As a special case, our approach can be applied to the stable module categories of arbitrary finite dimensional Hopf algebras that are not necessarily cocommutative (or quasitriangular). We illustrate the general theorems with classifications of the Balmer spectra and thick two-sided/right ideals for the stable module categories of all small quantum groups for Borel subalgebras, and classifications of the Balmer spectra and thick two-sided ideals of Hopf algebras studied by \textit{D. Benson} and \textit{S. Witherspoon} [Arch. Math. 102, No. 6, 513--520 (2014; Zbl 1310.16025)].Local quantum uncertainty for the thermal state of a four-qubit spin chain under decoherence channelshttps://zbmath.org/1517.810722023-09-22T14:21:46.120933Z"Tae-Hung, Ryang"https://zbmath.org/authors/?q=ai:tae-hung.ryang"Nam-Ung, Ri"https://zbmath.org/authors/?q=ai:nam-ung.ri"Pyong, Ri"https://zbmath.org/authors/?q=ai:pyong.ri"Chang-Rim, Sin"https://zbmath.org/authors/?q=ai:chang-rim.sin"Jong-Yon, Kim"https://zbmath.org/authors/?q=ai:jong-yon.kimSummary: We consider a four-qubit Heisenberg XY spin chain with Dzyaloshinskii-Moriya interaction. We use the local quantum uncertainty as a measure of nonclassical correlations to evaluate the thermal quantum correlations between two spins which are located at both ends of the chain. Also we study the behavior of local quantum uncertainty under dephasing, depolarizing and phase flip channels. Here, we demonstrate the effects of temperature, Heisenberg exchange interaction, Dzyaloshinskii-Moriya interaction, and decoherence parameters on local quantum uncertainty, and provide a way to increase or maximize the quantum correlations. The exchange interaction and the Dzyaloshinskii-Moriya interaction have the same effect on local quantum uncertainty. The results are irrespective of whether the considered system is ferromagnetic or antiferromagnetic.Towards super Teichmüller spin TQFThttps://zbmath.org/1517.810732023-09-22T14:21:46.120933Z"Aghaei, Nezhla"https://zbmath.org/authors/?q=ai:aghaei.nezhla"Pawelkiewicz, M. K."https://zbmath.org/authors/?q=ai:pawelkiewicz.m-k"Yamazaki, Masahito"https://zbmath.org/authors/?q=ai:yamazaki.masahitoSummary: The quantization of the Teichmüller theory has led to the formulation of the so-called Teichmüller TQFT for 3-manifolds. In this paper we initiate the study of ``supersymmetrization'' of the Teichmüller TQFT, which we call the super Teichmüller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichmüller spin TQFT for a class of spin 3-manifold geometries, by taking advantage of the recent results on the quantization of the super Teichmüller theory. We then compute the perturbative expansions of the partition functions, to obtain perturbative invariants of spin 3-manifolds. We also comment on the relations of the super Teichmüller spin TQFT to 3-dimensional Chern-Simons theories with complex gauge groups, and to a class of 3d \(\mathcal{N}=2\) theories arising from the compactifications of the M5-branes.The geometry and DSZ quantization four-dimensional supergravityhttps://zbmath.org/1517.810742023-09-22T14:21:46.120933Z"Lazaroiu, C."https://zbmath.org/authors/?q=ai:lazaroiu.calin-iuliu"Shahbazi, C. S."https://zbmath.org/authors/?q=ai:shahbazi.carlos-sSummary: We implement the Dirac-Schwinger-Zwanziger integrality condition on four-dimensional classical ungauged supergravity and use it to obtain its duality-covariant, gauge-theoretic, differential-geometric model on an oriented four-manifold \(M\) of arbitrary topology. Classical bosonic supergravity is completely determined by a submersion \(\pi\) over \(M\) equipped with a complete Ehresmann connection, a vertical Euclidean metric and a vertically polarized flat symplectic vector bundle \(\Xi\). Building on these structures, we implement the Dirac-Schwinger-Zwanziger integrality condition through the choice of an element in the degree-two sheaf cohomology group with coefficients in a locally constant sheaf \(\mathcal{L}\subset \Xi\) valued in the groupoid of integral symplectic spaces. We show that these data determine a Siegel principal bundle \(P_{\mathfrak{t}}\) of fixed type \(\mathfrak{t}\in \mathbb{Z}^{n_v}\) whose connections provide the global geometric description of the local electromagnetic gauge potentials of the theory. Furthermore, we prove that the Maxwell gauge equations of the theory reduce to the polarized self-duality condition determined by \(\Xi\) on the connections of \(P_{\mathfrak{t}}\). In addition, we investigate the continuous and discrete U-duality groups of the theory, characterizing them through short exact sequences and realizing the latter through the gauge group of \(P_{\mathfrak{t}}\) acting on its adjoint bundle. This elucidates the geometric origin of U-duality, which we explore in several examples, illustrating its dependence on the topology of the fiber bundles \(\pi\) and \(P_{\mathfrak{t}}\) as well as on the isomorphism type of \(\mathcal{L}\).Towards equivariant Yang-Mills theoryhttps://zbmath.org/1517.810752023-09-22T14:21:46.120933Z"Bonechi, F."https://zbmath.org/authors/?q=ai:bonechi.francesco"Cattaneo, A. S."https://zbmath.org/authors/?q=ai:cattaneo.alberto-sergio"Zabzine, M."https://zbmath.org/authors/?q=ai:zabzine.maximSummary: We study four dimensional gauge theories in the context of an equivariant extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial integration in the equivariant BV setting (BV push-forward map) is performed explicitly for the abelian case. As result, we obtain a non-local homological generalization of the Cartan calculus and a non-local extension of the abelian YM BV action which satisfies the equivariant master equation.Opers and the twisted Bogomolny equationshttps://zbmath.org/1517.810762023-09-22T14:21:46.120933Z"He, Siqi"https://zbmath.org/authors/?q=ai:he.siqi"Mazzeo, Rafe"https://zbmath.org/authors/?q=ai:mazzeo.rafe-rOriginally defined on a 4-dimensional oriented Riemannian manifold \(M^4\) together with a principal \(\mathrm{SU}(n)\)-bundle, the twisted Kapustin-Witten (TKW) equations are a one-parameter family of first-order equations which can be reduced to the 3-dimensional factor \(X\) in the case \(M^4=X\times\mathbb{R}_+\). The authors consider the reduced case when \(X=S^1\times\Sigma\) for some compact Riemann surface \(\Sigma\) and the solutions are assumed to be \(S^1\)-invariant. Then the TKW equations become the so-called twisted Bogomolny equations. Assuming the associated parameter to be different from 1, the authors focus on the map defined by \textit{D. Gaiotto} and \textit{E. Witten} [Adv. Theor. Math. Phys. 16, No. 3, 935--1086 (2012; Zbl 1271.81108)], which goes from the space of solutions to the twisted Bogomolny equations modulo gauge and with suitable boundary and pole conditions to the so-called twisted oper moduli space. Their main result is that this map is a diffeomorphism, which confirms a conjecture in [loc. cit.].
Reviewer: Nicolas Ginoux (Metz)Spin in particle physicshttps://zbmath.org/1517.810772023-09-22T14:21:46.120933Z"Leader, Elliot"https://zbmath.org/authors/?q=ai:leader.elliotPublisher's description: Motivated by dramatic developments in the field, this book provides a thorough introduction to spin and its role in elementary particle physics. Starting with a simple pedagogical introduction to spin and its relativistic generalisation, the author avoids the obscurity and impenetrability of traditional treatments of the subject. The book surveys the main theoretical and experimental developments, as well as discussing exciting plans for the future. Emphasis is placed on the importance of spin-dependent measurements in testing QCD and the Standard Model. This book will be of value to graduate students and researchers working in all areas of quantum physics and particularly in elementary particle and high energy physics. It is suitable as a supplementary text for graduate courses in theoretical and experimental particle physics. This title, first published in 2001, has been reissued as an Open Access publication on Cambridge Core.
See the review of the 2001 edition in [Zbl 0989.81070].Large \(N\) behaviour of the two-dimensional Yang-Mills partition functionhttps://zbmath.org/1517.810782023-09-22T14:21:46.120933Z"Lemoine, Thibaut"https://zbmath.org/authors/?q=ai:lemoine.thibautSummary: We compute the large \(N\) limit of the partition function of the Euclidean Yang-Mills measure on orientable compact surfaces with genus \(g\geqslant 1\) and non-orientable compact surfaces with genus \(g\geqslant 2\), with structure group the unitary group \(\mathrm{U}(N)\) or special unitary group \(\mathrm{SU}(N)\). Our proofs are based on asymptotic representation theory: more specifically, we control the dimension and Casimir number of irreducible representations of \(\mathrm{U}(N)\) and \(\mathrm{SU}(N)\) when \(N\) tends to infinity. Our main technical tool, involving `almost flat' Young diagram, makes rigorous the arguments used by \textit{D. J. Gross} and \textit{W. Taylor IV} [Nucl. Phys., B 400, No. 1--3, 181--208 (1993; Zbl 0941.81586)] in the setting of QCD, and in some cases, we recover formulae given by \textit{M. R. Douglas} [NATO ASI Ser., Ser. B, Phys. 328, 119--135 (1995; Zbl 0846.53062)] and \textit{B. Rusakov} [Phys. Lett. B 303, No. 1--2, 95--98 (1993; \url{doi:10.1016/0370-2693(93)90049-N})].Constraints in the BV formalism: six-dimensional supersymmetry and its twistshttps://zbmath.org/1517.810792023-09-22T14:21:46.120933Z"Saberi, Ingmar"https://zbmath.org/authors/?q=ai:saberi.ingmar-a"Williams, Brian R."https://zbmath.org/authors/?q=ai:williams.brian-rSummary: We formulate the abelian six-dimensional \(\mathcal{N} = (2, 0)\) theory perturbatively, in a generalization of the Batalin-Vilkovisky formalism. Using this description, we compute the holomorphic and non-minimal twists at the perturbative level. This calculation hinges on the existence of an \(L_\infty\) action of the supersymmetry algebra on the abelian tensor multiplet, which we describe in detail. Our formulation appears naturally in the pure spinor superfield formalism, but understanding it requires developing a presymplectic generalization of the BV formalism, inspired by Dirac's theory of constraints. The holomorphic twist consists of symplectic-valued holomorphic bosons from the \(\mathcal{N} = (1, 0)\) hypermultiplet, together with a degenerate holomorphic theory of holomorphic one-forms from the \(\mathcal{N} = (1, 0)\) tensor multiplet, which can be seen to describe the infinitesimal intermediate Jacobian variety. We check that our formulation and our results match with known ones under various dimensional reductions, as well as comparing the holomorphic twist to Kodaira-Spencer theory. Matching our formalism to five-dimensional Yang-Mills theory after reduction leads to some issues related to electric-magnetic duality; we offer some speculation on a nonperturbative resolution.Spectrum of the hypereclectic spin chain and Pólya countinghttps://zbmath.org/1517.810802023-09-22T14:21:46.120933Z"Ahn, Changrim"https://zbmath.org/authors/?q=ai:ahn.changrim"Staudacher, Matthias"https://zbmath.org/authors/?q=ai:staudacher.matthiasSummary: In earlier work we proposed a generating function that encodes the Jordan block spectrum of the integrable Hypereclectic spin chain, related to the one-loop dilatation operator of the dynamical fishnet quantum field theory. We significantly improve the expressions for these generating functions, rendering them much more explicit and elegant. In particular, we treat the case of the full spin chain without imposing any cyclicity constraints on the states, as well as the case of cyclic states. The latter involves the Pólya enumeration theorem in conjunction with \(q\)-binomial coefficients.Crosscap states in integrable field theories and spin chainshttps://zbmath.org/1517.810812023-09-22T14:21:46.120933Z"Caetano, João"https://zbmath.org/authors/?q=ai:caetano.joao"Komatsu, Shota"https://zbmath.org/authors/?q=ai:komatsu.shotaSummary: We study crosscap states in integrable field theories and spin chains in \(1+1\) dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the \textit{crosscap entropy}, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov's staircase model to flows between \(D\)-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.Branes, quivers, and the affine Grassmannianhttps://zbmath.org/1517.810822023-09-22T14:21:46.120933Z"Bourget, Antoine"https://zbmath.org/authors/?q=ai:bourget.antoine"Grimminger, Julius F."https://zbmath.org/authors/?q=ai:grimminger.julius-f"Hanany, Amihay"https://zbmath.org/authors/?q=ai:hanany.amihay"Sperling, Marcus"https://zbmath.org/authors/?q=ai:sperling.marcus"Zhong, Zhenghao"https://zbmath.org/authors/?q=ai:zhong.zhenghaoSummary: Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to study physical aspects of the affine Grassmannian. Explicit quivers are presented throughout the paper, and a quiver addition algorithm to generate the affine Grassmannian is introduced. An important outcome of this study is a set of quivers for new elementary slices.
For the entire collection see [Zbl 1516.14004].D-braneshttps://zbmath.org/1517.810832023-09-22T14:21:46.120933Z"Johnson, Clifford V."https://zbmath.org/authors/?q=ai:johnson.clifford-vPublisher's description: D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting their development in a pedagogical manner. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for other avenues of research. Suitable as a textbook in graduate courses on modern string theory and theoretical particle physics, it will also be an indispensable reference for seasoned practitioners. First published in 2003, this title has been reissued as an Open Access publication on Cambridge Core.
See the review of the 2003 edition in [Zbl 1026.81047].Twisted cohomotopy implies M5-brane anomaly cancellationhttps://zbmath.org/1517.810842023-09-22T14:21:46.120933Z"Sati, Hisham"https://zbmath.org/authors/?q=ai:sati.hisham"Schreiber, Urs"https://zbmath.org/authors/?q=ai:schreiber.ursSummary: We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then, we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted cohomotopy.Single-valued hyperlogarithms, correlation functions and closed string amplitudeshttps://zbmath.org/1517.810852023-09-22T14:21:46.120933Z"Vanhove, Pierre"https://zbmath.org/authors/?q=ai:vanhove.pierre"Zerbini, Federico"https://zbmath.org/authors/?q=ai:zerbini.federicoSummary: We give new proofs of a global and a local property of the integrals which compute closed string theory amplitudes at genus zero. Both kinds of properties are related to the newborn theory of singlevalued periods, and our proofs provide an intuitive understanding of this relation. The global property, known in physics as the KLT formula, is a factorisation of the closed string integrals into products of pairs of open string integrals. We deduce it by identifying closed string integrals with special values of single-valued correlation functions in two dimensional conformal field theory, and by obtaining their conformal block decomposition. The local property is of number theoretical nature. We write the asymptotic expansion coefficients as multiple integrals over the complex plane of special functions known as single-valued hyperlogarithms. We develop a theory of integration of single-valued hyperlogarithms, and we use it to demonstrate that the asymptotic expansion coefficients belong to the ring of single-valued multiple zeta values.Interacting massless infraparticles in 1+1 dimensionshttps://zbmath.org/1517.810862023-09-22T14:21:46.120933Z"Dybalski, Wojciech"https://zbmath.org/authors/?q=ai:dybalski.wojciech"Mund, Jens"https://zbmath.org/authors/?q=ai:mund.jensSummary: The Buchholz' scattering theory of waves in two dimensional massless models suggests a natural definition of a scattering amplitude. We compute such a scattering amplitude for charged infraparticles that live in the GNS representation of the \(2d\) massless scalar free field and obtain a non-trivial result. It turns out that these excitations exchange phases, depending on their charges, when they collide.Quantum entanglement and spectral form factorhttps://zbmath.org/1517.810872023-09-22T14:21:46.120933Z"Ma, Chen-Te"https://zbmath.org/authors/?q=ai:ma.chen-te"Wu, Chih-Hung"https://zbmath.org/authors/?q=ai:wu.chih-hungSummary: We replace a Hamiltonian with a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This study establishes a connection between quantities within Quantum Entanglement and Quantum Chaos. To have a universal study for Quantum Entanglement, we consider the Gaussian random 2-qubit model. The maximum violation of Bell's inequality demonstrates a positive correlation with the entanglement entropy. Thus, the violation plays an equivalent role as Quantum Entanglement. We first provide an analytical estimation of the relation between quantum entanglement quantities and the dip when a subregion only has one qubit. The time of the first dip is monotone for entanglement entropy. The dynamics in a subregion is independent of the initial state at a late time. It is one of the signaling conditions for classical chaos. We also extend our analysis to the Gaussian random 3-qubit state, and it indicates a similar result. The simulation shows that the level spacing distribution function approaches GUE at a late time. In the end, we develop a technique within QFT to the spectral form factor for its relation to an \(n\)-sheet manifold. We apply the technology to a single interval in \(CFT_2\) and the spherical entangling surface in \(\mathcal{N}=4\) super Yang-Mills theory. The result is one for both cases, but the Rényi entropy can depend on the Rényi index. For the case of \(CFT_2\), it indicates the difference between the continuum and discrete spectrum.General tensor structure for electron scattering in terms of invariant responseshttps://zbmath.org/1517.810882023-09-22T14:21:46.120933Z"Donnelly, T. W."https://zbmath.org/authors/?q=ai:donnelly.t-william"Jeschonnek, Sabine"https://zbmath.org/authors/?q=ai:jeschonnek.sabine"Van Orden, J. W."https://zbmath.org/authors/?q=ai:van-orden.j-wSummary: The use of invariant response functions in treatments of electron scattering from hadronic targets is reviewed. Various classes of reaction are treated, building from the simplest (and best known) case of inclusive scattering from unpolarized targets, to more complicated cases involving polarized electrons and possibly polarized spin-1/2 targets. In particular, the general structure of semi-inclusive polarized electron scattering from polarized spin-1/2 targets is emphasized. A summary is presented of how the leptonic and hadronic tensors that enter in the formalism are constructed in a general covariant way in terms of kinematic factors that are frame dependent but model independent and invariant response functions which contain all of the model-dependent dynamics. In the process of reviewing the general problem the relationships to the conventional responses expressed in terms of the frame-dependent helicity components of the exchanged virtual photon are presented.Unitarizing non-relativistic Coulomb scatteringhttps://zbmath.org/1517.810892023-09-22T14:21:46.120933Z"Oller, J. A."https://zbmath.org/authors/?q=ai:oller.jose-antonioSummary: We compare the exactly solvable nonrelativistic Coulomb scattering with two recent unitarization methods for infinite-range forces. These methods require to calculate perturbatively the corresponding partial-wave amplitudes, which are then unitarized. We calculate the Coulomb partial-wave amplitudes up to the one-loop order. On the one hand, the unitarization method developed by \textit{D. Blas} et al. [Phys. Lett., B 827, Article ID 136991, 7 p. (2022; Zbl 1487.83147); J. High Energy Phys. 2022, No. 8, Paper No. 266, 68 p. (2022; \url{doi:10.1007/JHEP08(2022)266})] reproduces properly the exact solution, with an accuracy improving as the order in the perturbative calculation of the input perturbative partial-wave amplitudes increases. This is also shown to be the case for the pole position of the ground state. On the other hand, the method developed by the more recent Ref. [\textit{R. L. Delgado} et al., Phys. Rev. D (3) 107, No. 4, Article ID 044073, 14 p. (2023; \url{doi:10.1103/PhysRevD.107.044073})] gives rise to partial-wave amplitudes that do not reproduce the known solvable solution, and gives rise to a pole position with zero binding energy.\(e^-e^+\to l^-l^+\) scattering in a strong magnetic field and LV backgroundhttps://zbmath.org/1517.810902023-09-22T14:21:46.120933Z"Sis, Mohammad Haghighi"https://zbmath.org/authors/?q=ai:sis.mohammad-haghighi"Mirza, Behrouz"https://zbmath.org/authors/?q=ai:mirza.behrouz"Sefidi, Arshin Khaje Borj"https://zbmath.org/authors/?q=ai:sefidi.arshin-khaje-borjSummary: We consider the Standard Model Extension (SME) by \(d_{\mu\nu}\) Lorentz violating parameter that can produce the electric dipole moment (EDM) and obtain the cross section of electron-positron to muon-anti-muon scattering in the presence of a strong magnetic field and the Lorentz violation (LV) background. The cross section has two terms; the second term is interesting and directly proportional to the magnitude of the magnetic field and the EDM of the particle. According to the last limits on EDM of muon, one cannot hope to discover the new physics even at \(2 Tev\) center of mass energies. But in the case of tau, around \(750 Gev\) center of mass energy, we expect to discover the effect of EDM. In the SME that the EDM of the particle is dependent on the Lorentz violation coefficient \(d_{\mu\nu}\) and the energy of the particle, it is expected that the effects of the EDM will be more noticeable at high energies. In this model, by the assumption that \(d_{\mu\nu}\) is \(9 \times 10^{-10}\) for muon and \(d_{\mu\nu}\) is \(2.2\times 1 0^{-5}\) for tau, the effect of EDM can be more visible in the limits of \(\sqrt{s}=500 GeV\) and \(\sqrt{s}=400 GeV\) respectively. Since many of the scatterings that occur in the cosmos are in strong magnetic fields and at high energies, the study of these scatterings contains important information for the analysis of cosmic phenomena.Analytic continuation of harmonic sums: dispersion representationhttps://zbmath.org/1517.810912023-09-22T14:21:46.120933Z"Velizhanin, V. N."https://zbmath.org/authors/?q=ai:velizhanin.v-nSummary: We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex arguments. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole expressions of these sums near negative integers. We describe the procedure for the precise numerical evaluations of the corresponding results from the dispersion representation.The \(\mathsf{CP}^{n-1}\)-model with fermions: a new lookhttps://zbmath.org/1517.810922023-09-22T14:21:46.120933Z"Bykov, Dmitri"https://zbmath.org/authors/?q=ai:bykov.dmitri-v.1|bykov.dmitri-vSummary: We elaborate the formulation of the \(\mathsf{CP}^{n-1}\) sigma model with fermions as a gauged Gross-Neveu model. This approach allows to identify the super phase space of the model as a supersymplectic quotient. Potential chiral gauge anomalies are shown to receive contributions from bosons and fermions alike and are related to properties of this phase space. Along the way we demonstrate that the worldsheet supersymmetric model is a supersymplectic quotient of a model with target space supersymmetry. Possible generalizations to other quiver supervarieties are briefly discussed.The quantum scale invariance in graphene-like quantum electrodynamicshttps://zbmath.org/1517.810932023-09-22T14:21:46.120933Z"Del Cima, O. M."https://zbmath.org/authors/?q=ai:del-cima.oswaldo-m"Franco, D. H. T."https://zbmath.org/authors/?q=ai:franco.daniel-h-t"Lima, L. S."https://zbmath.org/authors/?q=ai:lima.lazaro-s"Miranda, E. S."https://zbmath.org/authors/?q=ai:miranda.edilson-soaresSummary: The ultraviolet and infrared finiteness of a parity-even massless planar quantum electrodynamics mimics the scale invariance in graphene.Eliminating electron self-repulsionhttps://zbmath.org/1517.810942023-09-22T14:21:46.120933Z"Sebens, Charles T."https://zbmath.org/authors/?q=ai:sebens.charles-tSummary: Problems of self-interaction arise in both classical and quantum field theories. To understand how such problems are to be addressed in a quantum theory of the Dirac and electromagnetic fields (quantum electrodynamics), we can start by analyzing a classical theory of these fields. In such a classical field theory, the electron has a spread-out distribution of charge that avoids some of the problems of self-interaction facing point charge models. However, there remains the problem that the electron will experience self-repulsion. This self-repulsion cannot be eliminated within classical field theory without also losing Coulomb interactions between distinct particles. But, electron self-repulsion can be eliminated from quantum electrodynamics in the Coulomb gauge by fully normal-ordering the Coulomb term in the Hamiltonian. After normal-ordering, the Coulomb term contains pieces describing attraction and repulsion between distinct particles and also pieces describing particle creation and annihilation, but no pieces describing self-repulsion.Thermal leptophilic light vector dark matter with spinor mediator and muon \((g-2)\) anomalyhttps://zbmath.org/1517.810952023-09-22T14:21:46.120933Z"Ayazi, Seyed Yaser"https://zbmath.org/authors/?q=ai:ayazi.seyed-yaser"Mohamadnejad, Ahmad"https://zbmath.org/authors/?q=ai:mohamadnejad.ahmadSummary: Inspired by the recently new measurement of \((g-2)_\mu\) at FermiLab and reported upper bound for electron-dark matter (DM) recoil by the XENON1T collaboration, we revisited phenomenology of a light MeV scale vector dark matter in a leptophilic extension of standard model while a new spinor field plays the role of mediator. A viable parameter space is considered to discuss the possibility of light dark matter relic density as well as anomalous magnetic moment of the muon. We study DM-electron direct detection and cosmological bounds on the parameters space of the model. It is shown that although new bound of \((g - 2)_\mu\) anomaly greatly confines the parametric space of the model, the thermal light dark matter can exist for \(\text{M}_{\text{DM}} \sim 10^{-1}-10^1 \text{GeV}\).Constrained instanton approximation of skyrmions with massive pionshttps://zbmath.org/1517.810962023-09-22T14:21:46.120933Z"Martín-Caro, Alberto García"https://zbmath.org/authors/?q=ai:martin-caro.alberto-garciaSummary: We present the idea of using the holonomy along a line of a constrained instanton solution (an approximate solution of the Euclidean equations of motion subject to a constraint) of an \(SU(2)\) Yang-Mills-Higgs theory to approximate the Skyrmion solution in a chiral model with massive pions. The fact that the gauge field acquires a nonzero mass due to the Higgs mechanism implies that a constrained instanton decays exponentially far from its center, and so does the Skyrmion configuration that it generates via the Atiyah-Manton construction. This is precisely the desired behavior at large distances for the true Skyrmion solutions when the pion mass is included.Effect of the ensemble of cold atoms position in the Brillouin zone on the optical bistability and entanglement dynamicshttps://zbmath.org/1517.810972023-09-22T14:21:46.120933Z"Aggarwal, Neha"https://zbmath.org/authors/?q=ai:aggarwal.neha"Mahajan, Sonam"https://zbmath.org/authors/?q=ai:mahajan.sonam"Bhattacherjee, Aranya B."https://zbmath.org/authors/?q=ai:bhattacherjee.aranya-bSummary: We consider the dynamics of an ensemble of cold atoms coupled to light through radiation pressure in an optical lattice. We show that the steady-state displacement of the atomic ensemble shows bistable behavior which can be tuned by the position of the cold atoms in the Brillouin zone. Further, we describe a scheme to transfer the quantum state of the light field to the atomic field of two ensembles of cold atoms inside two independent optical cavities. This method leads to quantum entanglement which can be used in implementing quantum communication and computing. An Einstein-Podolsky-Rosen (EPR) state may be achieved with a judicious choice of parameters for our system.Symbolic-numeric algorithm for calculations in geometric collective model of atomic nucleihttps://zbmath.org/1517.810982023-09-22T14:21:46.120933Z"Deveikis, Algirdas"https://zbmath.org/authors/?q=ai:deveikis.algirdas"Gusev, Alexander A."https://zbmath.org/authors/?q=ai:gusev.alexander-a"Vinitsky, Sergue I."https://zbmath.org/authors/?q=ai:vinitsky.sergue-i"Blinkov, Yuri A."https://zbmath.org/authors/?q=ai:blinkov.yuri-a"Góźdź, Andrzej"https://zbmath.org/authors/?q=ai:gozdz.andrzej"Pȩdrak, Aleksandra"https://zbmath.org/authors/?q=ai:pedrak.aleksandra"Hess, Peter O."https://zbmath.org/authors/?q=ai:hess.peter-ottoSummary: We developed a symbolic-numeric algorithm involving a set of effective symbolic and numerical procedures for calculations of low lying energy spectra and eigenfunctions of atomic nuclei. The eigenfunctions are expanded over the orthonormal noncanonical \(U(5) {\supset } O(5) {\supset } O(3)\) basis in Geometric Collective Model. We give implementation of the algorithm and procedures in Wolfram Mathematica. We present benchmark calculations of energy spectrum, quadrupole moment and the reduced upwards transition probability B(E2) for the nucleus \(^{186}\)Os.
For the entire collection see [Zbl 1507.68024].Quantum sensing with sub-Planck structures for the dynamics of Bose-Einstein condensate in presence of engineered potential barriers inside a harmonic traphttps://zbmath.org/1517.810992023-09-22T14:21:46.120933Z"Bera, Jayanta"https://zbmath.org/authors/?q=ai:bera.jayanta-kr"Halder, Barun"https://zbmath.org/authors/?q=ai:halder.barun"Ghosh, Suranjana"https://zbmath.org/authors/?q=ai:ghosh.suranjana"Lee, Ray-Kuang"https://zbmath.org/authors/?q=ai:lee.ray-kuang"Roy, Utpal"https://zbmath.org/authors/?q=ai:roy.utpalSummary: We report a scheme for quantum sensing in ultracold atoms by utilizing an atom-interferometer producing sub-Planck scale structures. The condensate is trapped in a hybrid potential, comprising of an overall harmonic trap and sharp potential barriers which are designed as 50-50 atomic beam-splitters. A scaling law for quantum sensing is established for ultracold atoms and the maximum limit of quantum sensing is identified. Quantum sensing for position, momentum and temperature are demonstrated with a sufficiently stable condensate. The present scheme reveals maximum limit of quantum sensitivity for ultracold atoms against infinitesimal external perturbations. With a designable time sequence for the trapping potential, our results provide a promising scheme for quantum sensing with Bose-Einstein condensate in atomic chips.Corrigendum to: ``A generalization of the quantum Rabi model: exact solution and spectral structure''https://zbmath.org/1517.811002023-09-22T14:21:46.120933Z"Eckle, Hans-Peter"https://zbmath.org/authors/?q=ai:eckle.hans-peter"Johannesson, Henrik"https://zbmath.org/authors/?q=ai:johannesson.henrikFrom the text: Two of coefficients in equation (39) and (40) in the authors' paper [ibid. 50, No. 29, Article ID 294004, 23 p. (2017; Zbl 1370.81242)] were miscalculated and should be replaced. While the energy spectra in figures 5 and 6 of our original paper are numerically incorrect and should not be used for extracting quantitative information, the general conclusions drawn in the paper remain unchanged and valid. This includes the scenario for the lifting of degeneracies in the \(G\) functions illustrated in figure 2 of our original paper.Mechanical squeezing induced by Duffing nonlinearity and two driving tones in an optomechanical systemhttps://zbmath.org/1517.811012023-09-22T14:21:46.120933Z"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.263"Wang, Tie"https://zbmath.org/authors/?q=ai:wang.tie"Han, Xue"https://zbmath.org/authors/?q=ai:han.xue"Zhang, Shou"https://zbmath.org/authors/?q=ai:zhang.shou"Wang, Hong-Fu"https://zbmath.org/authors/?q=ai:wang.hongfuSummary: We propose a scheme to engineer strong steady-state mechanical squeezing via the joint effect between Duffing nonlinearity and two driving tones in an optomechanical system. It is found that the joint effect can achieve strong squeezing exceeding 3 dB when the amplitude ratio of two driving tones is large enough. Moreover, the generated squeezing can be flexibly manipulated by increasing the red-detuned laser power and selecting the amplitude ratio of two driving lasers. The robustness of mechanical squeezing set up by the joint effect to the thermal noise can be improved benefiting from the enhancement of red-detuned laser power. Furthermore, we present that the mechanical squeezing can be directly detected by homodyning the cavity output field under an appropriate phase.Nuclear superfluidity. Pairing in finite systemshttps://zbmath.org/1517.820042023-09-22T14:21:46.120933Z"Brink, David M."https://zbmath.org/authors/?q=ai:brink.david-m"Broglia, Ricardo A."https://zbmath.org/authors/?q=ai:broglia.ricardo-aPublisher's description: \textit{Nuclear Superfluidity} is a monograph devoted exclusively to pair correlations in nuclei. It begins by exploring pair correlations in a variety of systems including superconductivity in metals at low temperatures and superfluidity in liquid 3He and in neutron stars. The book goes on to introduce basic theoretical methods, symmetry breaking and symmetry restoration in finite many-body systems. The last few chapters are devoted to introducing results on the role of induced interactions in the structure of both normal and exotic nuclei. The most important of these is the renormalization of the pairing interaction due to the coupling of pairs of nucleons to low energy nuclear collective excitations. This book will be essential reading for researchers and students in experimental and theoretical nuclear physics, and related research fields such as metal clusters, fullerenes and quantum dots. This 2005 title has been reissued as an Open Access publication on Cambridge Core.
See the review of the original edition in [Zbl 1092.82049]. For the original paperback edition see [Zbl 1192.82085].Quantum statistics of identical particleshttps://zbmath.org/1517.820072023-09-22T14:21:46.120933Z"Garrison, J. C."https://zbmath.org/authors/?q=ai:garrison.john-cSummary: The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group.Universality of spin correlations in the Ising model on isoradial graphshttps://zbmath.org/1517.820122023-09-22T14:21:46.120933Z"Chelkak, Dmitry"https://zbmath.org/authors/?q=ai:chelkak.dmitry"Izyurov, Konstantin"https://zbmath.org/authors/?q=ai:izyurov.konstantin"Mahfouf, Rémy"https://zbmath.org/authors/?q=ai:mahfouf.remySummary: We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, that is, as the mesh size tends to zero at the same rate as the Baxter elliptic parameter tends to 1, the two-point spin correlations in the full plane converge to a universal rotationally invariant limit.
These results, together with techniques developed to obtain them, are sufficient to extend to isoradial graphs, the convergence results for multipoint spin correlations in bounded planar domains which were previously known only on the square grid. We also give a simple proof of the fact that the infinite-volume magnetization in a subcritical Z-invariant Ising model is independent of the site and of the lattice.
As compared to techniques already existing in the literature, we streamline the analysis of discrete (massive) holomorphic spinors near their ramification points which also provides a solid ground for further generalizations.Microscopical justification of the Winterbottom problem for well-separated latticeshttps://zbmath.org/1517.820182023-09-22T14:21:46.120933Z"Piovano, Paolo"https://zbmath.org/authors/?q=ai:piovano.paolo"Velčić, Igor"https://zbmath.org/authors/?q=ai:velcic.igorSummary: We consider the discrete atomistic setting introduced in [the authors, J. Nonlinear Sci. 32, No. 3, Paper No. 32, 55 p. (2022; Zbl 1489.82023)] to microscopically justify the continuum model related to the \textit{Winterbottom problem}, i.e., the problem of determining the equilibrium shape of crystalline film drops resting on a substrate, and relax the rigidity assumption considered in [loc. cit.] to characterize the \textit{wetting} and \textit{dewetting regimes} and to perform the \textit{discrete to continuum passage}. In particular, all results of the authors [loc. cit.] are extended to the setting where the distance between the reference lattices for the film and the substrate is not smaller than the optimal bond length between a film and a substrate atom. Such optimal film-substrate bonding distance is prescribed together with the optimal film-film distance by means of two-body atomistic interaction potentials of Heitmann-Radin type, which are both taken into account in the discrete energy, and in terms of which the wetting-regime threshold and the effective expression for the wetting parameter in the continuum energy are determined.Application of hierarchical equations of motion (HEOM) to time dependent quantum transport at zero and finite temperatureshttps://zbmath.org/1517.820262023-09-22T14:21:46.120933Z"Tian, Heng"https://zbmath.org/authors/?q=ai:tian.heng"Chen, GuanHua"https://zbmath.org/authors/?q=ai:chen.guanhuaSummary: Going beyond the limitations of our earlier works [\textit{X. Zheng} at al., ``Time-dependent density-functional theory for open systems'', Phys. Rev. B (3) 75, No. 19, Article 195127, 16 p. (2007, \url{doi:10.1103/PhysRevB.75.195127}); ``Time-dependent density functional theory for quantum transport'', J. Chem. Phys. 133, No. 11, Article ID 114101, 15 p. (2010; \url{doi:10.1063/1.3475566
})], we propose, in this manuscript, a new alternative approach to simulate time-dependent quantum transport phenomenon from first-principles. This new practical approach, still retaining the formal exactness of HEOM framework, does not rely on any intractable parametrization scheme and the pole structure of Fermi distribution function, thus, can seamlessly incorporated into first-principles simulation and treat transient response of an open electronic systems to an external bias voltage at both zero and finite temperatures on the equal footing. The salient feature of this approach is surveyed, and its time complexity is analysed. As a proof-of-principle of this approach, simulation of the transient current of one dimensional tight-binding chain, driven by some direct external voltages, is demonstrated.Jet quenching in glasmahttps://zbmath.org/1517.820342023-09-22T14:21:46.120933Z"Carrington, Margaret E."https://zbmath.org/authors/?q=ai:carrington.margaret-e"Czajka, Alina"https://zbmath.org/authors/?q=ai:czajka.alina"Mrówczyński, Stanisław"https://zbmath.org/authors/?q=ai:mrowczynski.stanislawSummary: We discuss the transverse momentum broadening of hard probes traversing an evolving glasma, which is the earliest phase of the matter produced in relativistic heavy-ion collisions. The coefficient \(\hat{q}\) is calculated using the Fokker-Planck equation, and an expansion in the proper time \(\tau\) which is applied to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision terms, which in turn provide \(\hat{q}\), are computed to fifth order in \(\tau\). The momentum broadening is shown to rapidly grow in time and reach a magnitude of several \(\mathrm{GeV}^2\)/fm. We show that the transient pre-equilibrium phase provides a contribution to the energy loss of hard probes which is comparable to that of the long lasting, hydrodynamically evolving, equilibrium phase.From charge to spin: analogies and differences in quantum transport coefficientshttps://zbmath.org/1517.820402023-09-22T14:21:46.120933Z"Marcelli, Giovanna"https://zbmath.org/authors/?q=ai:marcelli.giovanna"Monaco, Domenico"https://zbmath.org/authors/?q=ai:monaco.domenicoSummary: We review some recent results from the mathematical theory of transport of charge and spin in gapped crystalline quantum systems. The emphasis will be on transport coefficients, such as conductivities and conductances. As for the former, those are computed as appropriate expectations of current operators in a \textit{non-equilibrium almost-stationary state} (NEASS), which arises from the perturbation of an equilibrium state by an external electric field. While for charge transport the usual double-commutator Kubo formula is recovered (also beyond linear response), we obtain formulas for appropriately defined spin conductivities, which are still explicit but more involved. Certain ``Kubo-like'' terms in these formulas are also shown to agree with the corresponding contributions to the spin conductance. In addition to that, we employ similar techniques to show a new result, namely that even in systems with non-conserved spin, there is no generation of spin torque, that is, the spin torque operator has an expectation in the NEASS which vanishes faster than any power of the intensity of the perturbing field.
{\copyright 2022 American Institute of Physics}Theoretical and numerical investigations of the energy states and absorption coefficients of quantum dots and quantum anti-dots in the presence of a magnetic fieldhttps://zbmath.org/1517.820492023-09-22T14:21:46.120933Z"Rahimi, Fatemeh"https://zbmath.org/authors/?q=ai:rahimi.fatemeh"Ghaffary, Tooraj"https://zbmath.org/authors/?q=ai:ghaffary.toorajSummary: Present study focuses on analyzing the role of magnetic field on electronic spectra and absorption coefficients for the transitions \(1s\to 2p\) of \(GaAs/Ga_{1-x}Al_x As/GaAs\) spherical multilayer quantum dot (MLQD) and \(Ga_{1-x}Al_x As/GaAs/Ga_{1-x}Al_x As\) spherical multilayer quantum anti-dot (MLQAD) with hydrogenic impurity, via a comparative view. These nano structure systems have been studied both theoretically (Perturbation Theory), and numerically (Finite Difference Method). The wave functions and energy eigenvalues have been calculated using the finite difference method. In this paper it will be shown that a new degeneracy in presence of the uniform magnetic field in the MLQAD model will be appeared. Furthermore, the effects of the magnetic field, core radius size and potential confinement on \(1s\to 2p_0\) absorption coefficient and also on \(1s\) and \(2p\) energy states of these nano spherical structures have been discussed.Squeezed number state representation of the inflaton and particle production in the FRW universehttps://zbmath.org/1517.830032023-09-22T14:21:46.120933Z"Chand, Karam"https://zbmath.org/authors/?q=ai:chand.karamSummary: We use the single-mode coherent and squeezed number state formalism and analyze the nature of a massive homogeneous scalar field minimally coupled to gravity in the framework of semiclassical gravity in the Friedmann-Robertson-Walker (FRW) universe. We have obtained an estimate leading solution to the semiclassical Einstein equation for the FRW universe which shows the scale factor \(t^{2/3}\) power-law expansion. The mechanism of the particle production and quantum fluctuations are also analyzed in the FRW universe.Insights on entanglement entropy in \(1 + 1\) dimensional causal setshttps://zbmath.org/1517.830072023-09-22T14:21:46.120933Z"Keseman, Théo"https://zbmath.org/authors/?q=ai:keseman.theo"Muneesamy, Hans J."https://zbmath.org/authors/?q=ai:muneesamy.hans-j"Yazdi, Yasaman K."https://zbmath.org/authors/?q=ai:yazdi.yasaman-kSummary: Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a `truncation scheme'. This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a \(1 + 1\)D causal diamond in Minkowski spacetime. We present new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We extend previous results in the massless theory to include Rényi entropies and include new results for the massive theory. We also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.Exact instantons via worldline deformationshttps://zbmath.org/1517.830132023-09-22T14:21:46.120933Z"Akal, A."https://zbmath.org/authors/?q=ai:akal.aSummary: The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in certain cases. In this paper, we propose a novel technique allowing the construction of further exactly solvable models. In order to do so, we introduce a deformation function which maps the worldline instantons for a given model to the closed periodic stationary paths of a new model. Executing this procedure iteratively results in a chain of infinitely many solvable models. Similar ideas were applied to topological and nontopological defects in quantum field theory. We explicitly discuss the tunneling exponential in the Schwinger pair creation rate and illustrate the validity of the proposed technique for well-known cases.Relational analysis of Dirac equation in momentum representationhttps://zbmath.org/1517.830212023-09-22T14:21:46.120933Z"Solov'yov, Anton V."https://zbmath.org/authors/?q=ai:solovyov.anton-vSummary: In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a \textit{binary system of complex relations} (BSCR) between elements of two abstract sets. With the derivation performed, we show that the 4-dimensional pseudo-Euclidean momentum space is not needed \textit{a priori} but naturally emerges from considerations of rather general nature (2-spinor algebra). A bispinor wave function is constructed for a fermion with positive energy and an arbitrary distribution of momenta. Special attention is paid to physical assumptions that should be made to enable the construction.Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmologyhttps://zbmath.org/1517.830232023-09-22T14:21:46.120933Z"Han, Yu"https://zbmath.org/authors/?q=ai:han.yuSummary: The Hamiltonian constraint of scalar-tensor theories (STTs) in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The corresponding effective equations of motion derived from these effective Hamiltonian constraints turn out to be drastically different. The implications of each set of effective equations of motion are discussed in detail. In the latter half of this paper, as a concrete example, we study the effective dynamics of a specific model of STTs with the non-minimal coupling function \(F(\phi) = 1 + \xi\kappa\phi\) and self-interacting quartic potential. Using numerical results, we find different features for different effective dynamics. Moreover, it is also found that the spacetime singularity is absent and the cosmological bounce exists in each effective dynamics of this model.Infrared effects and the Unruh statehttps://zbmath.org/1517.830302023-09-22T14:21:46.120933Z"Anderson, Paul R."https://zbmath.org/authors/?q=ai:anderson.paul-r"Siahmazgi, Shohreh Gholizadeh"https://zbmath.org/authors/?q=ai:siahmazgi.shohreh-gholizadeh"Scofield, Zachary P."https://zbmath.org/authors/?q=ai:scofield.zachary-pSummary: Detailed behaviors of the modes of quantized scalar fields in the Unruh state for various eternal black holes in two dimensions are investigated. It is shown that the late-time behaviors of some of the modes of the quantum fields and of the symmetric two-point function are determined by infrared effects. The nature of these effects depends upon whether there is an effective potential in the mode equation and what form this potential takes. Here, three cases are considered, one with no potential and two with potentials that are nonnegative everywhere and are zero on the event horizon of the black hole and zero at either infinity or the cosmological horizon. Specifically, the potentials are a delta function potential and the potential that occurs for a massive scalar field in Schwarzschild-de Sitter spacetime. In both cases, scattering effects remove infrared divergences in the mode functions that would otherwise arise from the normalization process. When such infrared divergences are removed, it is found that the modes that are positive frequency with respect to the Kruskal time on the past black hole horizon approach zero in the limit that the radial coordinate is fixed and the time coordinate goes to infinity. In contrast, when there is no potential and thus infrared divergences occur, the same modes approach nonzero constant values in the late-time limit when the radial coordinate is held fixed. The behavior of the symmetric two-point function when the field is in the Unruh state is investigated for the case of a delta function potential in certain asymptotically flat black hole spacetimes in two dimensions. The removal of the infrared divergences in the mode functions results in the elimination of terms that grow linearly in time.Appell's correspondence unifies gravity with quantum theoryhttps://zbmath.org/1517.830312023-09-22T14:21:46.120933Z"Burinskii, Alexander"https://zbmath.org/authors/?q=ai:burinskii.alexanderSummary: Following Carter, Israel, López et al., we consider the over-rotating Kerr-Newman (KN) black hole solutions as classical gravitating electron models, formed by a relativistic ring string. We show that the Appell transformation establishes an unambiguous correspondence between a KN ring string written in Kerr-Schild coordinates and a point particle of quantum theory interacting with gravity on the Compton scale in agreement with QED. The Appell transformation doubles the Israel and López electron models, generalizing the classical ring string state to a quantum system forming the bare electron interacting with gravitating electron-positron vacuum. In the regularized version of the KN solution, the vector potential creates two quantum Wilson loops interacting with gravity, and the corresponding ring string currents create a magnetically bound monopole-antimonopole pair, establishing connections between the classical ring string solutions of the Einstein-Maxwell equations and the formalism of QED.Weakly isolated horizons: \(3+1\) decomposition and canonical formulations in self-dual variableshttps://zbmath.org/1517.830342023-09-22T14:21:46.120933Z"Corichi, Alejandro"https://zbmath.org/authors/?q=ai:corichi.alejandro"Reyes, Juan D."https://zbmath.org/authors/?q=ai:reyes.juan-d"Vukašinac, Tatjana"https://zbmath.org/authors/?q=ai:vukasinac.tatjanaSummary: The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy. In particular, the definition of weakly isolated horizons (WIHs) as quasilocal generalizations of event horizons is purely geometrical, and is independent of the variables used in describing the gravitational field. Here we consider a canonical decomposition of general relativity in terms of connection and vierbein variables starting from a first order action. Within this approach, the information about the existence of a (weakly) isolated horizon is obtained through a set of boundary conditions on an internal boundary of the spacetime region under consideration. We employ, for the self-dual action, a generalization of the Dirac algorithm for regions with boundary. While the formalism for treating gauge theories with boundaries is unambiguous, the choice of dynamical variables on the boundary is not. We explore this freedom and consider different canonical formulations for non-rotating black holes as defined by WIHs. We show that both the notion of horizon degrees of freedom and energy associated to the horizon is not unique, even when the descriptions might be self-consistent. This represents a generalization of previous work on isolated horizons both in the exploration of this freedom and in the type of horizons considered. We comment on previous results found in the literature.Null and timelike circular orbits from equivalent 2D metricshttps://zbmath.org/1517.830352023-09-22T14:21:46.120933Z"Cunha, Pedro V. P."https://zbmath.org/authors/?q=ai:cunha.pedro-v-p"Herdeiro, Carlos A. R."https://zbmath.org/authors/?q=ai:herdeiro.carlos-a-r"Novo, João P. A."https://zbmath.org/authors/?q=ai:novo.joao-p-aSummary: The motion of particles on spherical \(1+3\) dimensional spacetimes can, under some assumptions, be described by the curves on a two-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this paper we resort to auxiliary two-dimensional metrics to study circular geodesics of generic static, spherically symmetric, and asymptotically flat \(1+3\) dimensional spacetimes, whose functions are at least \(C^2\) smooth. This is done by studying the Gaussian curvature of the bidimensional equivalent manifold as well as the geodesic curvature of circular paths on these. This study considers both null and timelike circular geodesics. The study of null geodesics through the optical manifold retrieves the known result of the number of light rings on the spacetime outside a black hole and on spacetimes with horizonless compact objects. With an equivalent procedure we can formulate a similar theorem on the number of marginally stable timelike circular orbits of a given spacetime satisfying the previously mentioned assumptions.Vector boson oscillator in the near-horizon of the BTZ black holehttps://zbmath.org/1517.830392023-09-22T14:21:46.120933Z"Guvendi, Abdullah"https://zbmath.org/authors/?q=ai:guvendi.abdullah"Dogan, Semra Gurtas"https://zbmath.org/authors/?q=ai:dogan.semra-gurtasSummary: We investigate the interaction of a generalized vector boson oscillator with the near-horizon geometry of the Bañados-Teitelboim-Zanelli (BTZ) black hole and try to determine the corresponding quasibound state frequencies. To do this, we seek an analytical solution of the relativistic vector boson equation, derived as an excited state of Zitterbewegung, with Cornell-type non-minimal coupling in the near-horizon geometry of the BTZ black hole. The vector boson equation includes a symmetric spinor of rank two and this allows to obtain an analytical solution of the corresponding equation. By imposing appropriate boundary conditions, we show that it is possible to arrive at a relativistic frequency (\(\omega\)) expression in the form of \(\omega = \omega_{\mathcal{R}e} + \omega_{\mathcal{I}m}\). Our results show that real (\(\propto\omega_{\mathcal{R}e}\)) and damped (\(\propto\frac{1}{|\omega_{\mathcal{I}m}|}\)) oscillations depend on the parameters of the background geometry, coefficients of the non-minimal coupling and strength of the oscillator. This allows us to analyse the effects of both non-minimal coupling and spacetime parameters on the evolution of the considered vector field. We discuss the results in details and see also that the background is stable under the perturbation field in question.Bound orbits around charged black stringshttps://zbmath.org/1517.830402023-09-22T14:21:46.120933Z"Habibina, A. S."https://zbmath.org/authors/?q=ai:habibina.a-s"Ramadhan, H. S."https://zbmath.org/authors/?q=ai:ramadhan.handhika-sSummary: We study the geodesics of \(5d\) Reissner-Nordstrom and nonsingular black strings, and establish a rational bound orbit taxonomy for both massive as well as null test particles. For the timelike case, test particles with high energy (that would have made them plunge into or scatter off a black hole) could still form bound orbits around the black strings. We calculate the accumulated angles of the corresponding radial periods and show that they are higher than their \(4d\) counterparts. For the null case, we found the existence of stable null orbits outside their respective horizons, which do not exist in the four dimensions except at their extremal limit.Single-field model of gravitational-scalar instability. II: Black hole formationhttps://zbmath.org/1517.830422023-09-22T14:21:46.120933Z"Ignat'ev, Yu. G."https://zbmath.org/authors/?q=ai:ignatev.yu-gSummary: The previously formulated mathematical model of a statistical system with scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a one-component statistical system of scalarly charged degenerate fermions (\(\mathfrak{M}_1^c\) models), has led to the possibility of black hole formation in the early Universe using the mechanism of gravitational-scalar instability, which ensures the exponential growth of perturbations. The evolution of spherical masses in the \(\mathfrak{M}_1^c\) model, as well as the evolution of black holes with allowance for their evaporation, is studied. Arguments in favor of the possibility of black hole formation in the early Universe with the help of the proposed mechanism is given, and a numerical model is constructed that confirms this reasoning. The range of parameters of the \(\mathfrak{M}_1^c\) model, which ensures the growth of black hole masses in the early Universe up to \(10^4{-}10^6M_{\odot} \), is identified.
For Part I see [ibid. 28, No. 3, 275--291 (2022; Zbl 1511.83065)].Convergence of the Fefferman-Graham expansion and complex black hole anatomyhttps://zbmath.org/1517.830512023-09-22T14:21:46.120933Z"Serantes, Alexandre"https://zbmath.org/authors/?q=ai:serantes.alexandre"Withers, Benjamin"https://zbmath.org/authors/?q=ai:withers.benjaminSummary: Given a set of sources and one-point function data for a Lorentzian holographic QFT, does the Fefferman-Graham expansion converge? If it does, what sets the radius of convergence, and how much of the interior of the spacetime can be reconstructed using this expansion? As a step towards answering these questions we consider real analytic conformal field theory data, where in the absence of logarithms, the radius is set by singularities of the complex metric reached by analytically continuing the Fefferman-Graham radial coordinate. With the conformal boundary at the origin of the complex radial plane, real Lorentzian submanifolds appear as piecewise paths built from radial rays and arcs of circles centred on the origin. This allows singularities of Fefferman-Graham metric functions to be identified with gauge-invariant singularities of maximally extended black hole spacetimes, thereby clarifying the physical cause of the limited radius of convergence in such cases. We find black holes with spacelike singularities can give a radius of convergence equal to the horizon radius, however for black holes with timelike singularities the radius is smaller. We prove that a finite radius of convergence does not necessarily follow from the existence of an event horizon, a spacetime singularity, nor from caustics of the Fefferman-Graham gauge, by providing explicit examples of spacetimes with an infinite radius of convergence which contain such features.Non-local gravity wormholeshttps://zbmath.org/1517.830582023-09-22T14:21:46.120933Z"Capozziello, Salvatore"https://zbmath.org/authors/?q=ai:capozziello.salvatore"Godani, Nisha"https://zbmath.org/authors/?q=ai:godani.nishaSummary: We consider Non-local Gravity in view to obtain stable and traversable wormhole solutions. In particular, the class of Non-local Integral Kernel Theories of Gravity, with the inverse d'Alembert operator in the gravitational action, is taken into account. We obtain constraints for the null energy condition and derive the field equations. Two special cases for the related Klein-Gordan equation are assumed: one where the function in the gravitational action has a linear form and another one with exponential form. In each case, we take into account two forms for scalar fields and derive the shape functions. Asymptotic flatness and flaring-out conditions are checked. Energy conditions and dynamics of the solutions are examined at the throat. The main result is that non-local gravity contributions allow stability and traversability of the wormhole without considering any exotic matter.More on gravitational waves from double monodromy inflationhttps://zbmath.org/1517.830602023-09-22T14:21:46.120933Z"Abishev, Medeu"https://zbmath.org/authors/?q=ai:abishev.medeu"Abylayeva, Aigerim"https://zbmath.org/authors/?q=ai:abylayeva.aigerim"Addazi, Andrea"https://zbmath.org/authors/?q=ai:addazi.andrea"Aldabergenov, Yermek"https://zbmath.org/authors/?q=ai:aldabergenov.yermek"Berkimbayev, Daulet"https://zbmath.org/authors/?q=ai:berkimbayev.dauletSummary: We further analyze phenomenological implications of double axion monodromy inflation proposed in [\textit{G. D'Amico} et al.; Phys. Rev. D (3) 104, No. 8, Article ID L081302, 7 p. (2021; \url{doi:10.1103/PhysRevD.104.L081302})], in gravitational wave physics. We show that in addition to chiral gravitational waves (GW) originating from gauge field instability, the model also predicts significant amount of non-chiral, scalar-induced gravitational waves, both peaking at around the same frequencies. We find that although chiral GW density has much larger peak, non-chiral GWs can dominate away from the peak as they decay at a slower rate. This provides an interesting GW signature to be probed by future space-based interferometers such as LISA and DECIGO.Ruling out inflation driven by a power law potential: kinetic coupling does not helphttps://zbmath.org/1517.830612023-09-22T14:21:46.120933Z"Avdeev, N. A."https://zbmath.org/authors/?q=ai:avdeev.n-a"Toporensky, A. V."https://zbmath.org/authors/?q=ai:toporensky.alexey-vSummary: We demonstrate that the latest constraints on inflationary observables, namely, the tensor-to-scalar ratio \(r\) and the scalar spectral index \(n_S\) from the Cosmic Background Radiation (CMB) observations are already strong enough to rule out the model of a scalar field with a power law potential even in the presence of kinetic coupling to gravity with a positive coupling constant. The case for a negative coupling constant needs a special treatment.Nonlinear stability of self-gravitating massive fields. A wave-Klein-Gordon modelhttps://zbmath.org/1517.830632023-09-22T14:21:46.120933Z"LeFloch, Philippe G."https://zbmath.org/authors/?q=ai:lefloch.philippe-g"Ma, Yue"https://zbmath.org/authors/?q=ai:ma.yue.2Summary: In recent years, significant progress has been made in understanding the global evolution of self-gravitating massive matter in the small-perturbative regime near Minkowski spacetime. To investigate the interaction between a Klein-Gordon equation and Einstein's field equations, we developed a new approach called the Euclidean-hyperboloidal foliation method. This method involves constructing a spacetime foliation that is well-suited for deriving precise decay estimates for wave and Klein-Gordon equations in curved spacetime. In this article, we provide an overview of our method and present a complete proof for a wave-Klein-Gordon model that captures some of the key challenges associated with the Einstein-matter system.Magnetized quark and strange quark matter in the higher dimensional spherically symmetric space time admitting one parameter group of conformal motionshttps://zbmath.org/1517.830642023-09-22T14:21:46.120933Z"Kumbhare, Saroj R."https://zbmath.org/authors/?q=ai:kumbhare.saroj-r"Khadekar, G. S."https://zbmath.org/authors/?q=ai:khadekar.g-sSummary: In present paper, we have studied magnetized quark and strange quark matter with conformal motions in higher dimensional spherically symmetric space-time. We found Einstein's eld equations in higher dimensional spherically symmetric space-time using conformal motions. In the framework of higher dimension, various physical quantities have discussed.Lyapunov exponents in \(\mathcal{N} = 2\) supersymmetric Jackiw-Teitelboim gravityhttps://zbmath.org/1517.830662023-09-22T14:21:46.120933Z"Campos Delgado, Ruben"https://zbmath.org/authors/?q=ai:campos-delgado.ruben"Förste, Stefan"https://zbmath.org/authors/?q=ai:forste.stefanSummary: We study \(\mathcal{N} = 2\) supersymmetric Jackiw-Teitelboim (JT) gravity at finite temperature coupled to matter. The matter fields are related to superconformal primaries by AdS/CFT duality. Due to broken super reparametrisation invariance in the SCFT dual, there are corrections to superconformal correlators. These are generated by the exchange of super-Schwarzian modes which is dual to the exchange of 2D supergravity modes. We compute corrections to four-point functions for superconformal primaries and analyse the behaviour of out-of-time-ordered correlators. In particular, four-point functions of two pairs of primaries with mutually vanishing two-point functions are considered. By decomposing the corresponding supermultiplet into its components, we find different Lyapunov exponents. The value of the Lyapunov exponents depends on whether the correction is due to graviton, gravitini or graviphoton exchange. If mutual two-point functions do not vanish all components grow with maximal Lyapunov exponent.On-shell action for type IIB supergravity and superstrings on \(AdS_5 \times S^5\)https://zbmath.org/1517.830672023-09-22T14:21:46.120933Z"Chakrabarti, Subhroneel"https://zbmath.org/authors/?q=ai:chakrabarti.subhroneel"Gupta, Divyanshu"https://zbmath.org/authors/?q=ai:gupta.divyanshu"Manna, Arkajyoti"https://zbmath.org/authors/?q=ai:manna.arkajyotiSummary: AdS/CFT predicts that the value of the on-shell action for type IIB Supergravity (SUGRA) on \(AdS_5 \times S^5\) background must be a non-zero number completely determined from the boundary theory. We examine this statement within Sen's formalism for type IIB SUGRA and find that consistency with AdS/CFT requires us to add a specific boundary term to the action. We contrast our resolution with two other resolutions recently proposed in the literature in the context of different approaches to type IIB SUGRA. We explain how our resolution presents a strong benchmark for the possible boundary term of the complete spacetime action for type IIB superstring and how it may possibly lead to a piece of evidence for the strongest form of AdS/CFT conjecture in \(AdS_5 \times S^5\). We also comment on the fate of the on-shell action for general self-dual \(p\)-form fields in Sen's formalism in any curved backgrounds.Torsion-induced chiral magnetic current in equilibriumhttps://zbmath.org/1517.830692023-09-22T14:21:46.120933Z"Amitani, Tatsuya"https://zbmath.org/authors/?q=ai:amitani.tatsuya"Nishida, Yusuke"https://zbmath.org/authors/?q=ai:nishida.yusukeSummary: We study equilibrium transport properties of massless Dirac fermions at finite temperature and chemical potential in spacetime accompanied by torsion, which in four dimensions couples with Dirac fermions as an axial gauge field. In particular, we compute the current density at the linear order in the torsion as well as in an external magnetic field with the Pauli-Villars regulatization, finding that an equilibrium current akin to the chiral magnetic current is locally induced. Such torsion can be realized in condensed matter systems along a screw dislocation line, around which localized and extended current distributions are predicted so as to be relevant to Dirac and Weyl semimetals. Furthermore, we compute the current density at the linear order in the torsion as well as in a Weyl node separation, which turns out to vanish in spite of being allowed from the symmetry perspective. Contrasts of our findings with torsion-induced currents from previous work are also discussed.Transverse expansion of \((1 + 2)\) dimensional magneto-hydrodynamics flows with longitudinal boost invariancehttps://zbmath.org/1517.830752023-09-22T14:21:46.120933Z"Emamian, A."https://zbmath.org/authors/?q=ai:emamian.a"Kord, A. F."https://zbmath.org/authors/?q=ai:kord.a-f"Ghaani, A."https://zbmath.org/authors/?q=ai:ghaani.azam"Azadegan, B."https://zbmath.org/authors/?q=ai:azadegan.behnamSummary: In the present work, we investigate the effects of the magnetic field on expanding hot and dense nuclear matter as an ideal fluid. We consider QGP, in the particular case of a \((1 + 2)\) dimensional longitudinally boost-invariant fluid expansion, in the background of an inhomogeneous magnetic field that is generated by external sources. We assume the magnetic field points in the direction perpendicular to the reaction plane, follows the power-law decay in proper time, and has two components on the transverse plane. To simplify our calculation, we suppose the investigated fluid has azimuthal symmetry, and magneto-hydrodynamic equations are described in a polar coordinate system on the transverse plane of reaction. Our results depict the space-time evolution of the transverse expansion of the fluid in the presence of an inhomogeneous external magnetic field. Moreover, we show when the magnetic field decays in proper time \(\tau\) with a power-law \(\tau^n/2\) (\(n < 1\)), two distinct solutions can be found depending on the values of \(n\). We show that \(n < -2\) gives rise to the physical scenario whereas the \(n > -2\) leads to non-physical results.Photon propagation in a material medium on a curved spacetimehttps://zbmath.org/1517.830772023-09-22T14:21:46.120933Z"Guerrieri, Amanda"https://zbmath.org/authors/?q=ai:guerrieri.amanda"Novello, Mário"https://zbmath.org/authors/?q=ai:novello.marioSummary: We consider a nonlinear dielectric medium surrounding a static, charged and spherically symmetric compact body which gravitational field is driven by general relativity. Considering the propagating waves on the dielectric medium, we describe the trajectory of light as geodesics on an effective geometry given by Hadamard's discontinuities. We analyze some consequences of the effective geometry in the propagation of light, with relation to the predictions of the background gravitational field, that includes corrections on the geometrical redshift and on the gravitational deflection of light. We show that the background electromagnetic field polarize the material medium, such that different polarizations of light are distinguished by different corrections on these quantities. As a consequence, we have two possible paths for the trajectory of light in such configuration, that coincide if we turn off the electromagnetic field or if the permittivity is constant. We show that the effective metric associated to the negative polarization, for a given dependence of the dielectric permittivity, is conformally flat.Automorphic scalar fields in two-dimensional de Sitter spacehttps://zbmath.org/1517.830782023-09-22T14:21:46.120933Z"Higuchi, Atsushi"https://zbmath.org/authors/?q=ai:higuchi.atsushi"Schmieding, Lasse"https://zbmath.org/authors/?q=ai:schmieding.lasse"Serrano Blanco, David"https://zbmath.org/authors/?q=ai:serrano-blanco.davidSummary: We study non-interacting automorphic quantum scalar fields with positive mass in two-dimensional de Sitter space. We find that there are no Hadamard states which are de Sitter invariant except in the periodic case, extending the result of Epstein and Moschella for the anti-periodic case. We construct the two-point Wightman functions for the non-Hadamard de Sitter-invariant states by exploiting the fact that they are functions of the geodesic distance between the two points satisfying an ordinary differential equation. We then examine a certain Hadamard state, which is not de Sitter invariant, and show that it is approximately a thermal state with the Gibbons-Hawking temperature when restricted to a static region of the spacetime.Evaluating the spin-0 particle in Gurses rainbow universehttps://zbmath.org/1517.830792023-09-22T14:21:46.120933Z"Kangal, E. E."https://zbmath.org/authors/?q=ai:kangal.evrim-ersinSummary: In this study, we solved the Klein-Gordon's oscillator equation in Gurses rainbow universe. Subsequently, the energy quantization and associated wave function are obtained with the help of the Nikiforov-Uvarov technique. In the final stage, we compare graphically the rainbow effect with General Relativity (GR) one. According to the obtained result, the occurrence of asymmetrical breaking between positive and negative energy states has been observed in the rainbow scenario.Classical and quantum bicosmology with noncommutativityhttps://zbmath.org/1517.830802023-09-22T14:21:46.120933Z"Kan, Nahomi"https://zbmath.org/authors/?q=ai:kan.nahomi"Aoyama, Takuma"https://zbmath.org/authors/?q=ai:aoyama.takuma"Shiraishi, Kiyoshi"https://zbmath.org/authors/?q=ai:shiraishi.kiyoshiSummary: Recently, Falomir, Gamboa, Méndez, Gondolo and Maldonado proposed a bicosmology scenario for solving some cosmological problems related to inflation, dark matter, and thermal history of the Universe [\textit{H. Falomir} et al., Phys. Rev. D (3) 96, No. 8, Article ID 083534, 16 p. (2017; \url{doi:10.1103/PhysRevD.96.083534}); Phys. Lett., B 785, 399--402 (2018; Zbl 1398.83139); Symmetry 12, No. 3, Paper No. 435, 9 p. (2020; \url{doi:10.3390/sym12030435}); \textit{C. Maldonado} and \textit{F. Méndez}, Phys. Rev. D (3) 103, No. 12, Article ID 123505, 8 p. (2021; \url{doi:10.1103/PhysRevD.103.123505})]. Their plan is to introduce noncommutativity into the momentum space of the two scale factors. In the present paper, we revisit their model and first consider exact classical solutions in the model with constant noncommutativity between dynamical variables and between canonical momenta. We also hypothesize that the noncommutativity appears when the scale factors are small, and show the behavior of the classical solution in that case with momentum-space noncommutativity. Finally, we write down the Wheeler-DeWitt equation in that case and examine the behavior of the solution.Two fluids cosmological model in (2+1)-dimensional Saez-Ballester scalar-tensor theory of gravitationhttps://zbmath.org/1517.830822023-09-22T14:21:46.120933Z"Kumar, Praveen"https://zbmath.org/authors/?q=ai:kumar.praveen"Khadekar, G. S."https://zbmath.org/authors/?q=ai:khadekar.g-s"Dagwal, V. J."https://zbmath.org/authors/?q=ai:dagwal.v-jSummary: Two fluids cosmological models with matter and radiating source in \((2 + 1)\)-dimensional Saez-Ballester scalar-tensor theory of gravitation are investigated. In the two-fluid model, one fluid represent the CMB radiation and another fluid represent the matter content of the universe. To get determinate solution of the field equations we have consider the relation between pressure and energy density of the matter field through the gamma law equation of state \(p_m = (\gamma - 1) \rho_m\). Some physical and geometric behaviour of the models are also discussed with the uses of mathematical software.Thermal Casimir effect in Gödel-type universeshttps://zbmath.org/1517.830872023-09-22T14:21:46.120933Z"Santos, A. F."https://zbmath.org/authors/?q=ai:santos.alesandro-ferreira"Khanna, Faqir C."https://zbmath.org/authors/?q=ai:khanna.faqir-cSummary: In this paper, a massless scalar field coupled to gravity is considered. Then the Casimir effect at finite temperature is calculated. Such development is carried out in the Thermo Field Dynamics formalism. This approach presents a topological structure that allows for investigating the effects of temperature and the size effect in a similar way. These effects are calculated considering Gödel-type solutions as a gravitational background. The Stefan-Boltzmann law and its consistency are analyzed for both causal and non-causal Gödel-type regions. In this space-time and for any region, the Casimir effect at zero temperature is always attractive. However, at finite temperature, a repulsive Casimir effect can emerge from a critical temperature.Matter and space. New theory of fields and particleshttps://zbmath.org/1517.830892023-09-22T14:21:46.120933Z"Zhuravlev, V. M."https://zbmath.org/authors/?q=ai:zhuravlev.viktor-mikhailovichSummary: The paper presents a theory giving a unified geometric description of space and matter on the basis of a new concept related to general relativity (GR). The theory is built on the basis of a critical analysis of GR. The principle of materiality of space is introduced. The description of matter is based on the idea of space as a three-dimensional material hypersurface embedded in a four-dimensional Euclidean space. Matter particles are associated with extended areas of the material hypersurface, and their properties, such as charge and mass, with topological and geometric properties of this hypersurface. The central place in the mathematical apparatus for describing the material hypersurface itself and matter particles is played by marker fields, which are similar in essence to hydrodynamic markers used in classical hydrodynamics. Based on the theory of marker fields, questions of the topological structure of particles and connection between the electric charge and the topology of a material hypersurface are discussed. The mass of particles is represented as a property of the material hypersurface itself and has the meaning of gravitational and inertial mass at the same time. The fields, gravitational and electromagnetic, are properties of the material hypersurface geometry expressed in terms of marker fields. To describe the dynamics of particles, the geometric principle of averaging is introduced, which, as a result, leads to the equations of Newtonian mechanics and quantum theory.Building post-Newtonian neutron starshttps://zbmath.org/1517.850012023-09-22T14:21:46.120933Z"Andersson, Nils"https://zbmath.org/authors/?q=ai:andersson.nils"Gittins, Fabian"https://zbmath.org/authors/?q=ai:gittins.fabian"Yin, Shanshan"https://zbmath.org/authors/?q=ai:yin.shanshan"Macedo, Rodrigo Panosso"https://zbmath.org/authors/?q=ai:macedo.rodrigo-panossoSummary: Owed to their compactness, neutron stars involve strong gravity and extreme density physics. Nevertheless, at present, there are a variety of problems where progress (at least conceptually) can be made in the context of weak gravity. Motivated by this we examine how accurately one can model neutron stars using the post-Newtonian (pN) approximation to general relativity. In general, we find there is a significant degree of freedom in how the pN equations of stellar structure can be formulated. We discuss this flexibility in the formulation and provide examples to demonstrate the impact on stellar models. We also consider the (closely related) problem of building neutron stars using isotropic coordinates. In this context, we provide a new strategy for solving the equations (based on a scaling argument) which significantly simplifies the problem.Scalar correlators and normal modes in holographic neutron starshttps://zbmath.org/1517.850032023-09-22T14:21:46.120933Z"Canavesi, Tobías"https://zbmath.org/authors/?q=ai:canavesi.tobias"Fierro, Octavio"https://zbmath.org/authors/?q=ai:fierro.octavio"Grandi, Nicolás"https://zbmath.org/authors/?q=ai:grandi.nicolas-esteban"Pisani, Pablo"https://zbmath.org/authors/?q=ai:pisani.pablo-a-gSummary: The holographic neutron star provides a strong coupling description for a highly degenerate metallic state on a sphere. Its phase space can be split into two different sectors, with an unstable region at intermediate degeneracies. We investigate the critical nature of such region, by analyzing the asymptotic behavior of a scalar probe to compute the two-point correlator of the boundary theory. We show that in the stable region the correlator is dominated by the normal modes, whereas it displays a critical power-law behavior as we move into the unstable region.Impacts of symmetry energy slope on the oscillation frequencies of neutron stars with short-range correlation and admixed dark matterhttps://zbmath.org/1517.850062023-09-22T14:21:46.120933Z"Hong, Bin"https://zbmath.org/authors/?q=ai:hong.bin"Ren, ZhongZhou"https://zbmath.org/authors/?q=ai:ren.zhongzhou"Wu, Chen"https://zbmath.org/authors/?q=ai:wu.chen"Mu, XueLing"https://zbmath.org/authors/?q=ai:mu.xuelingSummary: Oscillation modes of compact stars, in general, can serve as a fingerprint in determining the equation of state (EOS) of dense matter. In this study, we examine the impact of symmetry energy slope (\(L\)) on the oscillation frequencies of neutron stars (NSs) with nucleon-nucleon short range correlation (SRC) and admixed dark matter (DM) for the first time within the relativistic mean-field theory. By adjusting the \(L\), we revise the EOS and coupling parameters in light of the SRC and DM effects, and construct the new sets. The results reveal that NSs containing SRC and DM inside are more likely to satisfy the observational constraints, and we find that smaller \(L\) exhibits larger fundamental non-radial and radial frequencies, and that the effect on large separation is also mainly concentrated in the low-mass region. Moreover, we update the linear relationship between the non-radial frequency and mean density, and we further give empirical relations between non-radial and radial frequencies and tidal deformability at different \(L\) for \(1.4M_\odot\) and \(2M_\odot\). These findings will enable us to more effectively confine the NS EOSs, in turn, also provide a strategy to place constraints on the \(L\).Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equationshttps://zbmath.org/1517.850072023-09-22T14:21:46.120933Z"Izquierdo, M. R."https://zbmath.org/authors/?q=ai:izquierdo.m-r"Pareschi, L."https://zbmath.org/authors/?q=ai:pareschi.lorenzo"Miñano, B."https://zbmath.org/authors/?q=ai:minano.borja"Massó, J."https://zbmath.org/authors/?q=ai:masso.joan"Palenzuela, C."https://zbmath.org/authors/?q=ai:palenzuela.carlosSummary: Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the \textit{grey} approximation, which reduces Boltzmann seven-dimensional equation to a system of \(3 + 1\) equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, high-order time integration schemes based on Implicit-Explicit Runge-Kutta methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit Runge-Kutta commonly employed for the magneto-hydrodynamics and Einstein equations. Finally, we analyze their performance in several numerical tests.The role of the electric bond number in the stability of pasta phaseshttps://zbmath.org/1517.850082023-09-22T14:21:46.120933Z"Kubis, Sebastian"https://zbmath.org/authors/?q=ai:kubis.sebastian"Wójcik, Włodzimierz"https://zbmath.org/authors/?q=ai:wojcik.wlodzimierzSummary: The deformation of nuclei in the neutrons star crust can be modelled by the system of two charged fluids separated by the phase boundary with non-zero surface tension. The stability of highly elongated structures, called pasta phases, is discussed here. In this work the cylindrical and spherical portion of charged fluids are considered. Their behavior depends on whether they are in vacuum or in charged surroundings what is modelled by Wigner-Seitz cell. The electric Bond number appears to be crucial parameter in the analysis. Variety of different unstable modes in vacuum case is strongly reduced in the case of W-S cell. It comes from the virial theorem, which bounds the value of the Bond number and reduces the role played by electric forces. Although the analysis is motivated by the nuclear pasta phases it can be applied to any system of two charged fluids.LRPC codes with multiple syndromes: near ideal-size KEMs without idealshttps://zbmath.org/1517.940472023-09-22T14:21:46.120933Z"Aguilar-Melchor, Carlos"https://zbmath.org/authors/?q=ai:aguilar-melchor.carlos"Aragon, Nicolas"https://zbmath.org/authors/?q=ai:aragon.nicolas"Dyseryn, Victor"https://zbmath.org/authors/?q=ai:dyseryn.victor"Gaborit, Philippe"https://zbmath.org/authors/?q=ai:gaborit.philippe"Zémor, Gilles"https://zbmath.org/authors/?q=ai:zemor.gillesSummary: We introduce a new rank-based key encapsulation mechanism (KEM) with public key and ciphertext sizes around 3.5 Kbytes each, for 128 bits of security, without using ideal structures. Such structures allow to compress objects, but give reductions to specific problems whose security is potentially weaker than for unstructured problems. To the best of our knowledge, our scheme improves in size upon all the existing unstructured post-quantum lattice or code-based algorithms such as FrodoKEM or Classic McEliece. Our technique, whose efficiency relies on properties of rank metric, is to build upon existing Low Rank Parity Check (LRPC) code-based KEMs and to send multiple syndromes in one ciphertext, allowing to reduce the parameters and still obtain an acceptable decoding failure rate. Our system relies on the hardness of the Rank Support Learning problem, a well-known variant of the Rank Syndrome Decoding problem. The gain on parameters is enough to significantly close the gap between ideal and non-ideal constructions. It also enables to choose an error weight close to the rank Gilbert-Varshamov bound, which is a relatively harder zone for algebraic attacks.
For the entire collection see [Zbl 1514.94001].Forward-secure revocable secret handshakes from latticeshttps://zbmath.org/1517.940522023-09-22T14:21:46.120933Z"An, Zhiyuan"https://zbmath.org/authors/?q=ai:an.zhiyuan"Pan, Jing"https://zbmath.org/authors/?q=ai:pan.jing"Wen, Yamin"https://zbmath.org/authors/?q=ai:wen.yamin"Zhang, Fangguo"https://zbmath.org/authors/?q=ai:zhang.fangguoSummary: Secret handshake \((\mathsf{SH})\), as a fundamental privacy-preserving primitive, allows members from the same organization to anonymously authenticate each other. Since its proposal by \textit{D. Balfanz} et al. [in: Proceedings of the 2003 IEEE symposium on security and privacy, Berkeley, CA, USA, Mai 13--14, 2003. Los Alamitos, CA: IEEE Computer Society. 180--196 (2003; \url{doi: 10.1109/SECPRI.2003.1199336})], numerous constructions have been proposed, among which only the ones separately designed by \textit{Z. Zhang} et al. [Lect. Notes Comput. Sci. 12309, 317--335 (2020; Zbl 1511.94164)] over coding and An et al. over lattice are secure against quantum attacks. However, none of known schemes consider the issue of key exposure, which is a common threat to cryptosystem implementations. To guarantee users' privacy against the key exposure attack, forward-secure mechanism is believed to be a promising countermeasure, where secret keys are periodically evolved in such a one-way manner that, past transactions of users are protected even if a break-in happens.
In this work we formalize the model of forward-secure secret handshake and present the first lattice-based instantiation, where ABB \(\mathsf{HIBE}\) is applied to handle key evolution process through regarding time periods as hierarchies. In particular, dynamic revocability is captured by upgrading the static verifier-local revocation techniques into updatable ones. To achieve anonymous handshake with ease, we present a generic way of transforming zero-knowledge argument systems termed as Fiat-Shamir with abort, into mutual authentication protocols. Our scheme is proved secure under the Short Integer Solution \((\mathsf{SIS})\) and Learning With Errors \((\mathsf{LWE})\) assumptions in the random oracle model.
For the entire collection see [Zbl 1514.94001].Improvement of algebraic attacks for solving superdetermined MinRank instanceshttps://zbmath.org/1517.940592023-09-22T14:21:46.120933Z"Bardet, Magali"https://zbmath.org/authors/?q=ai:bardet.magali"Bertin, Manon"https://zbmath.org/authors/?q=ai:bertin.manonSummary: The MinRank (MR) problem is a computational problem that arises in many cryptographic applications. In [\textit{J. Verbel} et al., Lect. Notes Comput. Sci. 11505, 167--186 (2019; Zbl 1509.94136)], the authors introduced a new way to solve superdetermined instances of the MinRank problem, starting from the bilinear Kipnis-Shamir (KS) modeling. They use linear algebra on specific Macaulay matrices, considering only multiples of the initial equations by one block of variables, the so called ``kernel'' variables. Later, \textit{M. Bardet} et al. [ibid. 12491, 507--536 (2020; Zbl 1511.94051)] introduced a new Support Minors modeling (SM), that consider the Plücker coordinates associated to the kernel variables, i.e. the maximal minors of the Kernel matrix in the KS modeling.
In this paper, we give a complete algebraic explanation of the link between the (KS) and (SM) modelings (for any instance). We then show that superdetermined MinRank instances can be seen as easy instances of the SM modeling. In particular, we show that performing computation at the smallest possible degree (the ``first degree fall'') and the smallest possible number of variables is not always the best strategy. We give complexity estimates of the attack for generic random instances.
We apply those results to the DAGS cryptosystem, that was submitted to the first round of the NIST standardization process. We show that the algebraic attack from \textit{É. Barelli} and \textit{A. Couvreur} [ibid. 11272, 93--118 (2018; Zbl 1446.94098)], improved in \textit{M. Bardet} et al. [ibid 11666, 86--101 (2019; \url{doi.org/10.1007/978-3-030-25922-8_5})], is a particular superdetermined MinRank instance. Here, the instances are not generic, but we show that it is possible to analyse the particular instances from DAGS and provide a way to select the optimal parameters (number of shortened positions) to solve a particular instance.
For the entire collection see [Zbl 1514.94001].Statistically sender-private OT from LPN and derandomizationhttps://zbmath.org/1517.940652023-09-22T14:21:46.120933Z"Bitansky, Nir"https://zbmath.org/authors/?q=ai:bitansky.nir"Freizeit, Sapir"https://zbmath.org/authors/?q=ai:freizeit.sapirSummary: We construct a two-message oblivious transfer protocol with statistical sender privacy (SSP OT) based on the Learning Parity with Noise (LPN) Assumption and a standard Nisan-Wigderson style derandomization assumption. Beyond being of interest on their own, SSP OT protocols have proven to be a powerful tool toward minimizing the round complexity in a wide array of cryptographic applications from proofs systems, through secure computation protocols, to hard problems in statistical zero knowledge (SZK).
The protocol is plausibly post-quantum secure. The only other constructions with plausible post quantum security are based on the Learning with Errors (LWE) Assumption. Lacking the geometric structure of LWE, our construction and analysis rely on a different set of techniques.
Technically, we first construct an SSP OT protocol in the common random string model from LPN alone, and then derandomize the common random string. Most of the technical difficulty lies in the first step. Here we prove a robustness property of the inner product randomness extractor to a certain type of linear splitting attacks. A caveat of our construction is that it relies on the so called low noise regime of LPN. This aligns with our current complexity-theoretic understanding of LPN, which only in the low noise regime is known to imply hardness in SZK.
For the entire collection see [Zbl 1514.94003].On actively secure fine-grained access structures from isogeny assumptionshttps://zbmath.org/1517.940752023-09-22T14:21:46.120933Z"Campos, Fabio"https://zbmath.org/authors/?q=ai:campos.fabio"Muth, Philipp"https://zbmath.org/authors/?q=ai:muth.philippSummary: We present an actively secure threshold scheme in the setting of Hard Homogeneous Spaces (HHS) which allows fine-grained access structures. More precisely, we elevate a passively secure isogeny-based threshold scheme to an actively secure setting. We prove the active security and simulatability of our advanced schemes. By characterising the necessary properties, we open our schemes to a significantly wider field of applicable secret sharing schemes. Furthermore, we show that Shamir's scheme has our generalised properties, and thereby our approach truly represents a less restrictive generalisation.
For the entire collection see [Zbl 1514.94001].IPRainbowhttps://zbmath.org/1517.940772023-09-22T14:21:46.120933Z"Cartor, Ryann"https://zbmath.org/authors/?q=ai:cartor.ryann"Cartor, Max"https://zbmath.org/authors/?q=ai:cartor.max"Lewis, Mark"https://zbmath.org/authors/?q=ai:lewis.mark-e|lewis.mark-l|lewis.mark-w|lewis.mark-a"Smith-Tone, Daniel"https://zbmath.org/authors/?q=ai:smith-tone.danielSummary: The Rainbow signature scheme is the only multivariate scheme listed as a finalist in round 3 of the NIST post-quantum standardization process. A few recent attacks, including the intersection attack, rectangular MinRank attacks, and the ``simple attack,'' have changed this landscape; leaving questions about the viability of this scheme for future application.
The purpose of this paper is to analyze the possibility of repairing Rainbow by adding an internal perturbation modifier and to compare its performance with that of UOV at the same security level. While the costly internal perturbation modifier was originally designed with encryption in mind, the use of schemes with performance characteristics similar to Rainbow is most interesting for applications in which short signatures or fast verification is a necessity, while signing can be done offline. We find that Rainbow can be made secure while achieving smaller keys, shorter signatures and faster verification times than UOV, but this advantage comes at significant cost in terms of signing time.
For the entire collection see [Zbl 1514.94001].Post-quantum signal key agreement from SIDHhttps://zbmath.org/1517.940932023-09-22T14:21:46.120933Z"Dobson, Samuel"https://zbmath.org/authors/?q=ai:dobson.samuel"Galbraith, Steven D."https://zbmath.org/authors/?q=ai:galbraith.steven-dSummary: In the effort to transition cryptographic primitives and protocols to quantum-resistant alternatives, an interesting and useful challenge is found in the Signal protocol. The initial key agreement component of this protocol, called X3DH, has so far proved more subtle to replace -- in part due to the unclear security model and properties the original protocol is designed for. This paper defines a formal security model for the original Signal protocol, in the context of the standard eCK and CK+ type models, which we call the Signal-adapted-CK model. We then propose a replacement for the Signal X3DH key exchange protocol based on SIDH, and provide a proof of security in the Signal-adapted-CK model, showing our protocol satisfies all security properties of the original Signal X3DH. We call this new protocol SI-X3DH. Our protocol shows that SIDH can be used to construct a secure X3DH replacement despite the existence of adaptive attacks against it. Unlike the generic constructions proposed in the literature, our protocol achieves deniability without expensive machinery such as post-quantum ring signatures. It also benefits from the small key sizes of SIDH, and its efficiency as a key-exchange protocol compared to other isogeny-based protocols such as CSIDH.
For the entire collection see [Zbl 1514.94001].Efficient NIZKs and signatures from commit-and-open protocols in the QROMhttps://zbmath.org/1517.940962023-09-22T14:21:46.120933Z"Don, Jelle"https://zbmath.org/authors/?q=ai:don.jelle"Fehr, Serge"https://zbmath.org/authors/?q=ai:fehr.serge"Majenz, Christian"https://zbmath.org/authors/?q=ai:majenz.christian"Schaffner, Christian"https://zbmath.org/authors/?q=ai:schaffner.christianSummary: Commit-and-open \(\Sigma \)-protocols are a popular class of protocols for constructing non-interactive zero-knowledge arguments and digital-signature schemes via the Fiat-Shamir transformation. Instantiated with hash-based commitments, the resulting non-interactive schemes enjoy tight online-extractability in the random oracle model. Online extractability improves the tightness of security proofs for the resulting digital-signature schemes by avoiding lossy rewinding or forking-lemma based extraction.
In this work, we prove tight online extractability in the quantum random oracle model (QROM), showing that the construction supports post-quantum security. First, we consider the default case where committing is done by element-wise hashing. In a second part, we extend our result to Merkle-tree based commitments. Our results yield a significant improvement of the provable post-quantum security of the digital-signature scheme Picnic.
Our analysis makes use of a recent framework by \textit{K.-M. Chung} et al. [Lect. Notes Comput. Sci. 12697, 598--629 (2021; Zbl 1479.94145)] for analysing quantum algorithms in the QROM using purely classical reasoning. Therefore, our results can to a large extent be understood and verified without prior knowledge of quantum information science.
For the entire collection see [Zbl 1514.94002].Estimating the hidden overheads in the BDGL lattice sieving algorithmhttps://zbmath.org/1517.940972023-09-22T14:21:46.120933Z"Ducas, Léo"https://zbmath.org/authors/?q=ai:ducas.leoSummary: The lattice sieving algorithm based on list-decoding of \textit{A. Becker} et al. [in: Proceedings of the 27th annual ACM-SIAM symposium on discrete algorithms, SODA 2016, Arlington, VA, USA, January 10--12, 2016. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); New York, NY: Association for Computing Machinery (ACM). 10--24 (2016; Zbl 1410.68093)] is currently at the center of cryptanalysis cost estimates of candidate lattice schemes for post-quantum standardization.
Yet, only an idealized version of this algorithm has been carefully modelled, i.e. given an efficient list-decoding oracle for a perfectly random spherical code. In this work, we propose an experimental analysis of the actual algorithm. The difficulty lies in estimating the probabilistic defect with respect to perfectly random spherical codes for the task at hand. While it should be in principle infeasible to run the algorithm in cryptographically relevant dimensions, a few tricks allow to nevertheless measure experimentally the relevant quantity.
Concretely, we conclude on an overhead factor of about \(2^6\) on the number of gates in the RAM model compared to the idealized model for dimensions around 380 after an appropriate re-parametrization. Part of this overhead can be traded for extra memory, at a costly rate. We also clarify that these overheads apply to an internal routine, and discuss how they can be partially mitigated in the whole attack.
For the entire collection see [Zbl 1514.94001].Partial key exposure attacks on BIKE, Rainbow and NTRUhttps://zbmath.org/1517.940992023-09-22T14:21:46.120933Z"Esser, Andre"https://zbmath.org/authors/?q=ai:esser.andre"May, Alexander"https://zbmath.org/authors/?q=ai:may.alexander"Verbel, Javier"https://zbmath.org/authors/?q=ai:verbel.javier-a"Wen, Weiqiang"https://zbmath.org/authors/?q=ai:wen.weiqiangSummary: In a so-called partial key exposure attack one obtains some information about the secret key, e.g. via some side-channel leakage. This information might be a certain fraction of the secret key bits (erasure model) or some erroneous version of the secret key (error model). The goal is to recover the secret key from the leaked information.
There is a common belief that, as opposed to e.g. the RSA cryptosystem, most post-quantum cryptosystems are usually resistant against partial key exposure attacks. We strongly question this belief by constructing partial key exposure attacks on code-based, multivariate, and lattice-based schemes (BIKE, Rainbow and NTRU). Our attacks exploit the redundancy that modern PQ cryptosystems inherently use for efficiency reasons. The application and development of techniques from information set decoding plays a crucial role for achieving our results.
On the theoretical side, we show non-trivial information leakage bounds that allow for a polynomial time key recovery attack. As an example, for all schemes the knowledge of a constant fraction of the secret key bits suffices to reconstruct the full key in polynomial time.
Even if we no longer insist on polynomial time attacks, most of our attacks extend well and remain feasible up to large erasure and error rates. In the case of BIKE for example we obtain attack complexities around 60 bits when half of the secret key bits are erased, or a quarter of the secret key bits are faulty.
Our results show that even highly error-prone key leakage of modern PQ cryptosystems may lead to full secret key recoveries.
For the entire collection see [Zbl 1514.94003].Attack on SHealS and HealS: the second wave of GPSThttps://zbmath.org/1517.941012023-09-22T14:21:46.120933Z"Galbraith, Steven D."https://zbmath.org/authors/?q=ai:galbraith.steven-d"Lai, Yi-Fu"https://zbmath.org/authors/?q=ai:lai.yi-fuSummary: We cryptanalyse the isogeny-based public key encryption schemes SHealS and HealS, and the key exchange scheme HealSIDH of \textit{T. B. Fouotsa} and \textit{C. Petit} [Lect. Notes Comput. Sci. 13093, 279--307 (2021; Zbl 1514.94082)].
For the entire collection see [Zbl 1514.94001].A new key recovery side-channel attack on HQC with chosen ciphertexthttps://zbmath.org/1517.941052023-09-22T14:21:46.120933Z"Goy, Guillaume"https://zbmath.org/authors/?q=ai:goy.guillaume"Loiseau, Antoine"https://zbmath.org/authors/?q=ai:loiseau.antoine"Gaborit, Philippe"https://zbmath.org/authors/?q=ai:gaborit.philippeSummary: Hamming Quasi-Cyclic (HQC) is a code-based candidate of NIST post-quantum standardization procedure. The decoding steps of code-based cryptosystems are known to be vulnerable to side-channel attacks and HQC is no exception to this rule. In this paper, we present a new key recovery side-channel attack on HQC with chosen ciphertext. Our attack takes advantage of the reuse of a static secret key on a micro-controller with a physical access. The goal is to retrieve the static secret key by targeting the Reed-Muller decoding step of the decapsulation and more precisely the Hadamard transform. This function is known for its diffusion property, a property that we exploit through side-channel analysis. The side-channel information is used to build an Oracle that distinguishes between several decoding patterns of the Reed-Muller codes. We show how to query the Oracle such that the responses give a full information about the static secret key. Experiments show that less than 20.000 electromagnetic attack traces are sufficient to retrieve the whole static secret key used for the decapsulation. Finally, we present a masking-based countermeasure to thwart our attack.
For the entire collection see [Zbl 1514.94001].How to backdoor (classic) McEliece and how to guard against backdoorshttps://zbmath.org/1517.941082023-09-22T14:21:46.120933Z"Hemmert, Tobias"https://zbmath.org/authors/?q=ai:hemmert.tobias"May, Alexander"https://zbmath.org/authors/?q=ai:may.alexander"Mittmann, Johannes"https://zbmath.org/authors/?q=ai:mittmann.johannes"Schneider, Carl Richard Theodor"https://zbmath.org/authors/?q=ai:schneider.carl-richard-theodorSummary: We show how to backdoor the McEliece cryptosystem such that a backdoored public key is indistinguishable from a usual public key, but allows to efficiently retrieve the underlying secret key.
For good cryptographic reasons, McEliece uses a small random seed \(\delta\) that generates via some pseudo random generator (PRG) the randomness that determines the secret key. Our backdoor mechanism works by encoding an encryption of \(\delta\) into the public key. Retrieving \(\delta\) then allows to efficiently recover the (backdoored) secret key. Interestingly, McEliece can be used itself to encrypt \(\delta\), thereby protecting our backdoor mechanism with strong post-quantum security guarantees.
Our construction also works for the current Classic McEliece NIST standard proposal for non-compressed secret keys, and therefore opens the door for widespread maliciously backdoored implementations.
Fortunately, our backdoor mechanism can be detected by the owner of the (backdoored) secret key if \(\delta\) is stored after key generation as specified by the Classic McEliece proposal. Thus, our results provide strong advice for implementers to store \(\delta\) inside the secret key and use \(\delta\) to guard against backdoor mechanisms.
For the entire collection see [Zbl 1514.94001].Sponge-based authenticated encryption: security against quantum attackershttps://zbmath.org/1517.941112023-09-22T14:21:46.120933Z"Janson, Christian"https://zbmath.org/authors/?q=ai:janson.christian"Struck, Patrick"https://zbmath.org/authors/?q=ai:struck.patrickSummary: In this work, we study the security of sponge-based authenticated encryption schemes against quantum attackers. In particular, we analyse the sponge-based authenticated encryption scheme \textsc{Slae} as put forward by \textit{J. P. Degabriele} et al. [Lect. Notes Comput. Sci. 11922, 209--240 (2019; Zbl 1456.94071)] due to its modularity. We show that the scheme achieves security in the post-quantum (QS1) setting in the quantum random oracle model by using the one-way to hiding lemma. Furthermore, we analyse the scheme in a fully-quantum (QS2) setting. There we provide a set of attacks showing that \textsc{Slae} does not achieve ciphertext indistinguishability and hence overall does not provide the desired level of security.
For the entire collection see [Zbl 1514.94001].Efficiently masking polynomial inversion at arbitrary orderhttps://zbmath.org/1517.941212023-09-22T14:21:46.120933Z"Krausz, Markus"https://zbmath.org/authors/?q=ai:krausz.markus"Land, Georg"https://zbmath.org/authors/?q=ai:land.georg"Richter-Brockmann, Jan"https://zbmath.org/authors/?q=ai:richter-brockmann.jan"Güneysu, Tim"https://zbmath.org/authors/?q=ai:guneysu.timSummary: Physical side-channel analysis poses a huge threat to post-quantum cryptographic schemes implemented on embedded devices. Still, secure implementations are missing for many schemes. In this paper, we present an efficient solution for masked polynomial inversion, a main component of the key generation of multiple post-quantum Key Encapsulation Mechanisms (KEMs). For this, we introduce a polynomial-multiplicative masking scheme with efficient arbitrary order conversions from and to additive masking. Furthermore, we show how to integrate polynomial inversion and multiplication into the masking schemes to reduce costs considerably. We demonstrate the performance of our algorithms for two different post-quantum cryptographic schemes on the Cortex-M4. For NTRU, we measure an overhead of 35\% for the first-order masked inversion compared to the unmasked inversion while for BIKE the overhead is as little as 11\%. Lastly, we verify the security of our algorithms for the first masking order by measuring and performing a TVLA based side-channel analysis.
For the entire collection see [Zbl 1514.94001].New complexity estimation on the rainbow-band-separation attackhttps://zbmath.org/1517.941362023-09-22T14:21:46.120933Z"Nakamura, Shuhei"https://zbmath.org/authors/?q=ai:nakamura.shuhei"Ikematsu, Yasuhiko"https://zbmath.org/authors/?q=ai:ikematsu.yasuhiko"Wang, Yacheng"https://zbmath.org/authors/?q=ai:wang.yacheng"Ding, Jintai"https://zbmath.org/authors/?q=ai:ding.jintai"Takagi, Tsuyoshi"https://zbmath.org/authors/?q=ai:takagi.tsuyoshiSummary: Multivariate public key cryptography is a candidate for post-quantum cryptography, and it allows generating particularly short signatures and fast verification. The Rainbow signature scheme proposed by \textit{J. Ding} and \textit{D. Schmidt} [Lect. Notes Comput. Sci. 3531, 164--175 (2005; Zbl 1126.68393)] is such a multivariate cryptosystem, and it is considered secure against all known attacks. The Rainbow-Band-Separation attack recovers a secret key of Rainbow by solving certain systems of quadratic equations, and its complexity is estimated by the well-known theoretical value called the degree of regularity. However, the degree of regularity is generally larger than the solving degree in experiments, and an accurate estimation cannot be obtained. In this article, we propose a new theoretical value for the complexity of the Rainbow-Band-Separation attack using a Gröbner basis algorithm, which provides a more precise estimation compared to that using the degree of regularity. This theoretical value is deduced by the two-variable power series \(\frac{ \prod_{i = 1}^m ( 1 - t_1^{d_{i 1}} t_2^{d_{i 2}} )}{ ( 1 - t_1 )^{n_1} ( 1 - t_2 )^{n_2}} .\) Since the two-variable power series coincides with the one-variable power series at \(t_1 = t_2\) deriving the degree of regularity, the theoretical value is less than or equal to the degree of regularity under a certain condition. Moreover, we show a relation between the Rainbow-Band-Separation attack using the hybrid approach and the HighRank attack. By considering this relation and our theoretical value, we obtain a new complexity estimation for the Rainbow-Band-Separation attack. Furthermore, applying our theoretical value to the complexity formula used in the NIST PQC 2nd round, we show that a slight modification of the proposed Rainbow parameter sets is required. Consequently, we provide a new theoretical value for generally estimating the solving degree of a bi-graded polynomial system, which can influence the parameter selection of Rainbow in the NIST PQC standardization project.Simplified MITM modeling for permutations: new (quantum) attackshttps://zbmath.org/1517.941522023-09-22T14:21:46.120933Z"Schrottenloher, André"https://zbmath.org/authors/?q=ai:schrottenloher.andre"Stevens, Marc"https://zbmath.org/authors/?q=ai:stevens.marcSummary: Meet-in-the-middle (MITM) is a general paradigm where internal states are computed along two independent paths (`forwards' and `backwards') that are then matched. Over time, MITM attacks improved using more refined techniques and exploiting additional freedoms and structure, which makes it more involved to find and optimize such attacks. This has led to the use of detailed attack models for generic solvers to automatically search for improved attacks, notably a MILP model developed by \textit{Z. Bao} et al. [Lect. Notes Comput. Sci. 12696, 771--804 (2021; Zbl 1479.94121)].
In this paper, we study a simpler MILP modeling combining a greatly reduced attack representation as input to the generic solver, together with a theoretical analysis that, for any solution, proves the existence and complexity of a detailed attack. This modeling allows to find both classical and quantum attacks on a broad class of cryptographic permutations. First, Present-like constructions, with the permutations from the Spongent hash functions: we improve the MITM step in distinguishers by up to 3 rounds. Second, AES-like designs: despite being much simpler than Bao et al.'s [loc. cit.], our model allows to recover the best previous results. The only limitation is that we do not use degrees of freedom from the key schedule. Third, we show that the model can be extended to target more permutations, like Feistel networks. In this context we give new Guess-and-determine attacks on reduced \textsf{Simpira v2} and \textsc{Sparkle}.
Finally, using our model, we find several new quantum preimage and pseudo-preimage attacks (e.g. \textsf{Haraka v2}, \textsf{Simpira v2}\dots) targeting the same number of rounds as the classical attacks.
For the entire collection see [Zbl 1514.94003].2F -- a new method for constructing efficient multivariate encryption schemeshttps://zbmath.org/1517.941582023-09-22T14:21:46.120933Z"Smith-Tone, Daniel"https://zbmath.org/authors/?q=ai:smith-tone.danielSummary: The Support Minors method of solving the MinRank problem has contributed to several new cryptanalyses of post-quantum cryptosystems including some of the most efficient multivariate cryptosystems. While there are a few viable multivariate schemes that are secure against rank methods, the most prominent schemes, particularly for encryption, are not particularly efficient.
In this article we present a new generic construction for building efficient multivariate encryption schemes. Such schemes can be built from maps having rank properties that would otherwise be damaging, but are immune to traditional rank attack. We then construct one such efficient multivariate encryption scheme and show it to be about 100 times faster than other secure multivariate encryption schemes in the literature.
For the entire collection see [Zbl 1514.94001].CPA/CCA2-secure PKE with squared-exponential DFR from low-noise LPNhttps://zbmath.org/1517.941642023-09-22T14:21:46.120933Z"Xu, Shengfeng"https://zbmath.org/authors/?q=ai:xu.shengfeng"Li, Xiangxue"https://zbmath.org/authors/?q=ai:li.xiangxue"Qian, Haifeng"https://zbmath.org/authors/?q=ai:qian.haifeng"Chen, Kefei"https://zbmath.org/authors/?q=ai:chen.kefeiSummary: LPN (learning parity with noise) problem is a good candidate for post-quantum cryptography which enjoys simplicity and suitability for weak-power devices. \textit{N. Döttling} et al. [Lect. Notes Comput. Sci. 7658, 485--503 (2012; Zbl 1292.94056)] initiated the first secure public key encryption (PKE) under the low-noise LPN assumption. \textit{E. Kiltz} et al. [ibid. 8383, 1--18 (2014; Zbl 1335.94059)] proposed a simpler and more efficient scheme using double-trapdoor technique from the same assumption. Both schemes abide the decoding failure rate (DFR) \( 2^{- {\Theta} ( k )}\) (\(k\) is the security parameter) and there exists CPA/CCA2-secure PKE with squared-exponential DFR \(2^{- {\Theta} ( k^2 )}\) from constant-noise LPN [\textit{Y. Yu} and \textit{J. Zhang}, Lect. Notes Comput. Sci. 9814, 214--243 (2016; Zbl 1378.94071)]. In this work, we give a positive answer with squared-exponential DFR in the low-noise setting.
More precisely, we first introduce a variant (VxLPN) of the low-noise Exact LPN (xLPN, proposed by \textit{A. Jain} et al. [ibid. 7658, 663--680 (2012; Zbl 1292.94082)] and used as building block in commitments and zero-knowledge proofs), where the coefficient matrix \(\mathfrak{A}\) follows the uniform distribution over \(\{ 0 , 1 \}^{q \times n}\) (\(n = {\Theta}( k^2)\), \(q = {\Theta}(n)\)), the secret \(\mathfrak{x}\) is sampled from \(\mathcal{B}_\mu^n\) (\(\mathcal{B}_\mu\) is the Bernoulli distribution with noise rate \(\mu = {\Theta}(\frac{ 1}{ \sqrt{ q}}))\), and the noise \(\mathfrak{e}\) follows a column vector distribution uniform over \(\{\mathfrak{z} \in \{ 0 , 1 \}^q : | \mathfrak{z} | = q \mu \} \). A series of reductions show that VxLPN is at least as hard as the standard LPN for the same noise rate \(\mu \). We then construct from the VxLPN CPA/CCA2 secure PKE schemes with squared-exponential DFR \(2^{- {\Theta} ( k^2 )}\) which share the common structure extrinsically with Kiltz et al. [loc. cit.] and Yu-Zhang schemes [loc. cit.]. The secret key(s) in our schemes are simply sampled from the Bernoulli distribution, and comparatively, the secret key(s) in Yu-Zhang schemes must be chosen from a tailored version of Bernoulli distribution (along with the coefficient matrix \(\mathfrak{A}\) that follows a distribution \(\mathcal{D}_\lambda^{n \times n} = U_{n \times \lambda} \cdot U_{\lambda \times n}\) induced by multiplying two random matrices in the public key, \( \lambda = {\Theta}( \log^2 n))\) in order to guarantee the correctness of their schemes. Consider the performance on 128-bit security level, our CCA2-secure scheme only holds 117.79 MB public keys, 67.31 MB secret keys and 10.15 KB ciphertexts, and thus is more efficient than the schemes of Döttling et al. [loc. cit.] and Kiltz et al. [loc. cit.] ((14.53 GB, 14.48 GB, 14.06 KB) and (161.78 MB, 92.45 MB, 13.60 KB) respectively).MR-DSS -- smaller MinRank-based (ring-)signatureshttps://zbmath.org/1517.941802023-09-22T14:21:46.120933Z"Bellini, Emanuele"https://zbmath.org/authors/?q=ai:bellini.emanuele"Esser, Andre"https://zbmath.org/authors/?q=ai:esser.andre"Sanna, Carlo"https://zbmath.org/authors/?q=ai:sanna.carlo"Verbel, Javier"https://zbmath.org/authors/?q=ai:verbel.javier-aSummary: In the light of NIST's announced reopening of the call for digital signature proposals in 2023 due to lacking diversity, there is a strong need for constructions based on other established hardness assumptions. In this work we construct a new post-quantum secure digital signature scheme based on the \textit{MinRank} problem, a problem with a long history of applications in cryptanalysis that led to a strong belief in its hardness. Initially following a design by \textit{N. T. Courtois} [Lect. Notes Comput. Sci. 2248, 402--421 (2001; Zbl 1064.94544)] based on the Fiat-Shamir transform, we make use of several recent developments in the design of sigma protocols to reduce signature size and improve efficiency. This includes the recently introduced sigma protocol with helper paradigm [\textit{W. Beullens}, ibid. 12107, 183--211 (2020; Zbl 1479.94295)] and combinations with cut-and-choose techniques. Moreover, we introduce several improvements to the core of the scheme to further reduce its signature size.
As a second contribution, we formalize the natural extension of our construction to a ring signature scheme and show that it achieves desired anonymity and unforgeability guarantees. Our ring signature is characterized by a sublinear scaling of the signature size in the number of users. Moreover, we achieve competitive practical signature sizes for moderate amount of users in comparison to recent ring signature proposals.
For the entire collection see [Zbl 1514.94001].Breaking rainbow takes a weekend on a laptophttps://zbmath.org/1517.941812023-09-22T14:21:46.120933Z"Beullens, Ward"https://zbmath.org/authors/?q=ai:beullens.wardSummary: This work introduces new key recovery attacks against the Rainbow signature scheme, which is one of the three finalist signature schemes still in the NIST Post-Quantum Cryptography standardization project. The new attacks outperform previously known attacks for all the parameter sets submitted to NIST and make a key-recovery practical for the SL 1 parameters. Concretely, given a Rainbow public key for the SL 1 parameters of the second-round submission, our attack returns the corresponding secret key after on average 53 h (one weekend) of computation time on a standard laptop.
For the entire collection see [Zbl 1514.94002].Delegating signing rights in a multivariate proxy signature schemehttps://zbmath.org/1517.941882023-09-22T14:21:46.120933Z"Debnath, Sumit Kumar"https://zbmath.org/authors/?q=ai:debnath.sumit-kumar"Choudhury, Tanmay"https://zbmath.org/authors/?q=ai:choudhury.tanmay"Stănică, Pantelimon"https://zbmath.org/authors/?q=ai:stanica.pantelimon"Dey, Kunal"https://zbmath.org/authors/?q=ai:dey.kunal"Kundu, Nibedita"https://zbmath.org/authors/?q=ai:kundu.nibeditaSummary: In the context of digital signatures, the proxy signature holds a significant role of enabling an original signer to delegate its signing ability to another party (i.e., proxy signer). It has significant practical applications. Particularly it is useful in distributed systems, where delegation of authentication rights is quite common. For example, key sharing protocol, grid computing, and mobile communications. Currently, a large portion of existing proxy signature schemes are based on the hardness of problems like integer factoring, discrete logarithms, and/or elliptic curve discrete logarithms. However, with the rising of quantum computers, the problem of prime factorization and discrete logarithm will be solvable in polynomial-time, due to Shor's algorithm [\textit{P. W. Shor}, SIAM Rev. 41, No. 2, 303--332 (1999; Zbl 1005.11507)], which dilutes the security features of existing ElGamal, RSA, ECC, and the proxy signature schemes based on these problems. As a consequence, construction of secure and efficient post-quantum proxy signature becomes necessary. In this work, we develop a post-quantum proxy signature scheme Mult-proxy, relying on multivariate public key cryptography (MPKC), which is one of the most promising candidates of post-quantum cryptography. We employ a 5-pass identification protocol to design our proxy signature scheme. Our work attains the usual proxy criterion and a one-more-unforgeability criterion under the hardness of the Multivariate Quadratic polynomial (MQ) problem. It produces optimal size proxy signatures and optimal size proxy shares in the field of MPKC.A new fault attack on UOV multivariate signature schemehttps://zbmath.org/1517.941912023-09-22T14:21:46.120933Z"Furue, Hiroki"https://zbmath.org/authors/?q=ai:furue.hiroki"Kiyomura, Yutaro"https://zbmath.org/authors/?q=ai:kiyomura.yutaro"Nagasawa, Tatsuya"https://zbmath.org/authors/?q=ai:nagasawa.tatsuya"Takagi, Tsuyoshi"https://zbmath.org/authors/?q=ai:takagi.tsuyoshiSummary: The unbalanced oil and vinegar signature scheme (UOV), which is one of the multivariate signature schemes, is expected to be secure against quantum attacks. To achieve cryptosystem security in a practical manner, we need to deal with security against physical attacks such as fault attacks, which generate computational errors to lead to security failures. In this study, we propose a new fault attack on UOV using faults occurring on the secret key. The proposed attack first recovers a part of the linear map of the secret key by utilizing faults occurring on the secret key, and then transforms the public key system. As a result, the proposed attack reduces a given public key system into one with fewer variables than the original system. After applying our proposed attack, the secret key can be recovered with less complexity than the original system by using an existing key recovery attack. Our simulation results show that, for two practical parameter sets satisfying 100-bit security, the proposed attack can reduce the given system into one with only 90-bit security with a probability of approximately \(80\sim 90\)\%. We also show that the proposed attack achieves a smaller resulting system than the above case with lower probability, and that such a system can be broken even more efficiently.
For the entire collection see [Zbl 1514.94001].