Recent zbMATH articles in MSC 81https://zbmath.org/atom/cc/812022-09-13T20:28:31.338867ZUnknown authorWerkzeugBook review of: L. Lovász, Graphs and geometryhttps://zbmath.org/1491.000162022-09-13T20:28:31.338867Z"Meunier, Frédéric"https://zbmath.org/authors/?q=ai:meunier.fredericReview of [Zbl 1425.05001].The logic induced by effect algebrashttps://zbmath.org/1491.030812022-09-13T20:28:31.338867Z"Chajda, Ivan"https://zbmath.org/authors/?q=ai:chajda.ivan"Halaš, Radomír"https://zbmath.org/authors/?q=ai:halas.radomir"Länger, Helmut"https://zbmath.org/authors/?q=ai:langer.helmut-mSummary: Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras \({\mathbf{E}} \), we investigate a natural implication and prove that the implication reduct of \({\mathbf{E}}\) is term equivalent to \({\mathbf{E}} \). Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered, we introduce a certain kind of implication which is everywhere defined but whose result need not be a single element. Then, we study effect implication algebras and prove the correspondence between these algebras and effect algebras satisfying the ascending chain condition. We present an axiom system in Gentzen style also for not necessarily lattice-ordered effect algebras and prove that it is an algebraic semantics for the logic induced by finite effect algebras.Laplacian pretty good fractional revivalhttps://zbmath.org/1491.051222022-09-13T20:28:31.338867Z"Chan, Ada"https://zbmath.org/authors/?q=ai:chan.ada"Johnson, Bobae"https://zbmath.org/authors/?q=ai:johnson.bobae"Liu, Mengzhen"https://zbmath.org/authors/?q=ai:liu.mengzhen"Schmidt, Malena"https://zbmath.org/authors/?q=ai:schmidt.malena"Yin, Zhanghan"https://zbmath.org/authors/?q=ai:yin.zhanghan"Zhan, Hanmeng"https://zbmath.org/authors/?q=ai:zhan.hanmengSummary: We develop the theory of pretty good fractional revival in quantum walks on graphs using their Laplacian matrices as the Hamiltonian. We classify the paths and the double stars that have Laplacian pretty good fractional revival.On residuation in paraorthomodular latticeshttps://zbmath.org/1491.060132022-09-13T20:28:31.338867Z"Chajda, I."https://zbmath.org/authors/?q=ai:chajda.ivan"Fazio, D."https://zbmath.org/authors/?q=ai:fazio.davideSummary: Paraorthomodular lattices are quantum structures of prominent importance within the framework of the logico-algebraic approach to (unsharp) quantum theory. However, at the present time it is not clear whether the above algebras may be regarded as the algebraic semantic of a logic in its own right. In this paper, we start the investigation of material implications in paraorthomodular lattices by showing that any bounded modular lattice with antitone involution \({\mathbf{A}}\) can be converted into a left-residuated groupoid if it satisfies a strengthened form of regularity. Moreover, the above condition turns out to be also necessary whenever \({\mathbf{A}}\) is distributive.An equational theory for \(\sigma \)-complete orthomodular latticeshttps://zbmath.org/1491.060152022-09-13T20:28:31.338867Z"Freytes, Hector"https://zbmath.org/authors/?q=ai:freytes.hectorSummary: The condition of \(\sigma \)-completeness related to orthomodular lattices places an important role in the study of quantum probability theory. In the framework of algebras with infinitary operations, an equational theory for the category of \(\sigma \)-complete orthomodular lattices is given. In this structure, we study the congruences theory and directly irreducible algebras establishing an equational completeness theorem. Finally, a Hilbert style calculus related to \(\sigma \)-complete orthomodular lattices is introduced and a completeness theorem is obtained.Orthomodular lattices as \(L\)-algebrashttps://zbmath.org/1491.060172022-09-13T20:28:31.338867Z"Wu, Yali"https://zbmath.org/authors/?q=ai:wu.yali"Yang, Yichuan"https://zbmath.org/authors/?q=ai:yang.yi-chuan|yang.yichuanSummary: We first prove that the axioms system of orthomodular \(L\)-algebra (\(O\)-\(L\)-algebras for short) as given in [\textit{W. Rump}, Forum Math. 30, No. 4, 973--995 (2018; Zbl 1443.06005)] are not independent by giving an independent axiom one. Then, two conditions for \textit{KL}-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure of \(OM \)-\(L\)-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.Basic algebras and L-algebrashttps://zbmath.org/1491.060332022-09-13T20:28:31.338867Z"Wang, Jing"https://zbmath.org/authors/?q=ai:wang.jing.18"Wu, Yali"https://zbmath.org/authors/?q=ai:wu.yali"Yang, Yichuan"https://zbmath.org/authors/?q=ai:yang.yi-chuan|yang.yichuanSummary: In this paper, we study the relation between L-algebras and basic algebras. In particular, we construct a lattice-ordered effect algebra which improves an example of \textit{I. Chajda} et al. [Algebra Univers. 60, No. 1, 63--90 (2009; Zbl 1219.06013)].Module constructions for certain subgroups of the largest Mathieu grouphttps://zbmath.org/1491.110502022-09-13T20:28:31.338867Z"Beneish, Lea"https://zbmath.org/authors/?q=ai:beneish.leaSummary: For certain subgroups of \(M_{24}\), we give vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of Mathieu moonshine. The construction is related to the Conway moonshine module and employs a technique introduced by Anagiannis-Cheng-Harrison [\textit{V. Anagiannis} et al., Commun. Math. Phys. 366, No. 2, 647--680 (2019; Zbl 1411.81157)]. With this construction we are able to give concrete vertex algebraic realizations of certain cuspidal Hecke eigenforms of weight two. In particular, we give explicit realizations of trace functions whose integralities are equivalent to divisibility conditions on the number of \(\mathbb{F}_p\) points on the Jacobians of modular curves.On the algebraicity about the Hodge numbers of the Hilbert schemes of algebraic surfaceshttps://zbmath.org/1491.140072022-09-13T20:28:31.338867Z"Jin, Seokho"https://zbmath.org/authors/?q=ai:jin.seokho"Jo, Sihun"https://zbmath.org/authors/?q=ai:jo.sihunSummary: Hilbert schemes are an object arising from geometry and are closely related to physics and modular forms. Recently, there have been investigations from number theorists about the Betti numbers and Hodge numbers of the Hilbert schemes of points of an algebraic surface. In this paper, we prove that Göttsche's generating function of the Hodge numbers of Hilbert schemes of \(n\) points of an algebraic surface is algebraic at a CM point \(\tau\) and rational numbers \(z_1\) and \(z_2\). Our result gives a refinement of the algebraicity on Betti numbers.Correction to: ``On the unitary block-decomposability of 1-parameter matrix flows and static matrices''https://zbmath.org/1491.150182022-09-13T20:28:31.338867Z"Uhlig, Frank"https://zbmath.org/authors/?q=ai:uhlig.frankCorrection to the author's paper [ibid. 89, No. 2, 529--549 (2022; Zbl 1486.15019)].A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equationhttps://zbmath.org/1491.160352022-09-13T20:28:31.338867Z"Gateva-Ivanova, Tatiana"https://zbmath.org/authors/?q=ai:gateva-ivanova.tatianaSummary: We study noninvolutive set-theoretic solutions \((X,r)\) of the Yang-Baxter equations in terms of the properties of the canonically associated braided monoid \(S(X,r)\), the quadratic Yang-Baxter algebra \(A= A(\mathbf{k}, X, r)\) over a field \(\mathbf{k} \), and its Koszul dual \(A^!\). More generally, we continue our systematic study of \textit{nondegenerate quadratic sets} \((X,r)\) \textit{and their associated algebraic objects}. Next we investigate the class of (noninvolutive) square-free solutions \((X,r)\). This contains the self distributive solutions (quandles). We make a detailed characterization in terms of various algebraic and combinatorial properties each of which shows the contrast between involutive and noninvolutive square-free solutions. We introduce and study a class of finite square-free braided sets \((X,r)\) of order \(n\geq 3\) which satisfy \textit{the minimality condition}, that is, \( \dim_{\mathbf{k}} A_2 =2n-1\). Examples are some simple racks of prime order \(p\). Finally, we discuss general extensions of solutions and introduce the notion of \textit{a generalized strong twisted union of braided sets}. We prove that if \((Z,r)\) is a nondegenerate \(2\)-cancellative braided set splitting as a generalized strong twisted union of \(r\)-invariant subsets \(Z = X\mathbin{\natural}^{\ast} Y\), then its braided monoid \(S_Z\) is a generalized strong twisted union \(S_Z= S_X\mathbin{\natural}^{\ast} S_Y\) of the braided monoids \(S_X\) and \(S_Y\). We propose a construction of a generalized strong twisted union \(Z = X\mathbin{\natural}^{\ast} Y\) of braided sets \((X,r_X)\) and \((Y,r_Y)\), where the map \(r\) has a high, explicitly prescribed order.Manin matrices for quadratic algebrashttps://zbmath.org/1491.160362022-09-13T20:28:31.338867Z"Silantyev, Alexey"https://zbmath.org/authors/?q=ai:silantyev.alexeySummary: We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of the category theory. The notion of minors is generalised for a general Manin matrix. We give some examples of Manin matrices, their relations with Lax operators and obtain the formulae for some minors. In particular, we consider Manin matrices of the types \(B, C\) and \(D\) introduced by \textit{A. Molev} [Sugawara operators for classical Lie algebras. Providence, RI: American Mathematical Society (AMS) (2018; Zbl 1395.17001)] and their relation with Brauer algebras. Infinite-dimensional Manin matrices and their connection with Lax operators are also considered.A class of non-weight modules of \(U_p(\mathfrak{s} \mathfrak{l}_2)\) and Clebsch-Gordan type formulashttps://zbmath.org/1491.170082022-09-13T20:28:31.338867Z"Cai, Yan-an"https://zbmath.org/authors/?q=ai:cai.yanan"Chen, Hongjia"https://zbmath.org/authors/?q=ai:chen.hongjia"Guo, Xiangqian"https://zbmath.org/authors/?q=ai:guo.xiangqian"Ma, Yao"https://zbmath.org/authors/?q=ai:ma.yao"Zhu, Mianmian"https://zbmath.org/authors/?q=ai:zhu.mianmianQuantum groups were initially constructed by Drinfeld, and independently by Jimbo, to study (quantum) Yang-Baxter equations. Given a finite-dimensional semisimple Lie algebra \(\mathfrak{g}\), the quantum group \(U_q(\mathfrak{g})\) is a Hopf algebra that depends on a parameter \(q\in \mathbb{C}\setminus \{0\}\), which is a deformation of the universal enveloping algebra \(U(\mathfrak{g})\).
The present authors construct a class of modules for the quantum group \(U_q(\mathfrak{sl}_2)\), which is free of rank \(1\) when restricted to \(\mathbb{C}[K^{\pm 1}]\); it corresponds to the universal enveloping algebra of the Cartan subalgebra of \(\mathfrak{sl}_2\). They prove that any \(\mathbb{C}[K^{\pm 1}]\)-free \(U_q(\mathfrak{sl}_2)\)-module of rank \(1\) is isomorphic to one of the modules they constructed (Theorem 3.2, page 747), and their isomorphism classes are obtained (Corollary 3.3, page 748). They also investigate the tensor products of the \(\mathbb{C}[K^{\pm 1}]\)-free modules with finite-dimensional simple modules over \(U_q(\mathfrak{sl}_2)\). For the generic cases, they obtain direct sum decomposition formulas for them, which are similar to the well-known Clebsch-Gordan formula for tensor products between finite-dimensional weight modules over \(U_q(\mathfrak{sl}_2)\) (Theorem 4.2, page 750).
Reviewer: Mee Seong Im (Annapolis)Chu duality theory and coalgebraic representation of quantum symmetrieshttps://zbmath.org/1491.180152022-09-13T20:28:31.338867Z"Maruyama, Yoshihiro"https://zbmath.org/authors/?q=ai:maruyama.yoshihiroSummary: Building upon \textit{V. Pratt}'s work [``The Stone Gamut: a coordinatization of mathematics'', in: Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science, LICS 95. Los Alamitos, CA: IEEE Computer Society. 444--454 (1995)] on applications of Chu space theory to Stone duality, we develop a general theory of categorical dualities on the basis of Chu space theory and closure conditions, which encompasses a variety of dualities for topological spaces, convex spaces, closure spaces, and measurable spaces (some of which are new duality results on their own). It works as a general method to generate analogues of categorical dualities between frames (locales) and topological spaces beyond topology, e.g., for measurable spaces, convex spaces, and closure spaces. After establishing the Chu duality theory, we apply the state-observable duality between quantum lattices and closure spaces to coalgebraic representations of quantum symmetries, showing that the quantum symmetry groupoid fully embeds into a purely coalgebraic category, i.e., the category of Born coalgebras, which refines, through the quantum duality that follows from Chu duality theory, Samson Abramsky's fibred coalgebraic representations of quantum symmetries [\textit{S. Abramsky}, J. Philos. Log. 42, No. 3, 551--574 (2013; Zbl 1270.81040)] (which, in turn, builds upon his Chu representations of symmetries).Hopfological algebra for infinite dimensional Hopf algebrashttps://zbmath.org/1491.180222022-09-13T20:28:31.338867Z"Farinati, Marco A."https://zbmath.org/authors/?q=ai:farinati.marco-aAt first, we need point out that Hopfological algebra is not a particular algebra system. Actually, this terminology is introduced by \textit{M. Khovanov} [J. Knot Theory Ramifications 25, No. 3, Article ID 1640006, 26 p. (2016; Zbl 1370.18017)] to mean the mixture of homological algebra and the theory of Hopf algebras. In particular, using some particular Hopf algebras to study homological algebra and consider applications, for example, application in categorification questions. \textit{Y. Qi} [Compos. Math. 150, No. 1, 1--45 (2014; Zbl 1343.16010)] developed this theory systematically through using some particular finite-dimensional Hopf algebras. And the paper under reviewed want to generalize above theory to co-Frobenius Hopf algebras, in particular, allows us to consider some infinite-dimensional Hopf algebras.
Reviewer: Liu Gongxiang (Nanjing)Asymptotic estimation for eigenvalues in the exponential potential and for zeros of \(K_{\mathrm{i}\nu} (z)\) with respect to orderhttps://zbmath.org/1491.330052022-09-13T20:28:31.338867Z"Krynytskyi, Yuri"https://zbmath.org/authors/?q=ai:krynytskyi.yuri"Rovenchak, Andrij"https://zbmath.org/authors/?q=ai:rovenchak.andrijSummary: The paper presents the derivation of the asymptotic behavior of \(\nu\)-zeros of the modified Bessel function of imaginary order \(K_{\mathrm{i}\nu} (z)\). This derivation is based on the quasiclassical treatment of the exponential potential on the positive half axis. The asymptotic expression for the \(\nu\)-zeros (zeros with respect to order) contains the Lambert \(W\) function, which is readily available in most computer algebra systems and numerical software packages. The use of this function provides much higher accuracy of the estimation comparing to known relations containing the logarithm, which is just the leading term of \(W(x)\) at large \(x\). Our result ensures accuracy sufficient for practical applications.Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentialshttps://zbmath.org/1491.351502022-09-13T20:28:31.338867Z"Rabinovich, Vladimir"https://zbmath.org/authors/?q=ai:rabinovich.vladimir-l|rabinovich.vladimir-sIn the paper, the 3D-Dirac operators with singular potentials supported on both bounded and unbounded surfaces in \(\mathbb{R}^3\) are considered. The approach to the self-adjointness of Dirac operators is based on the study of transmission problems with parameter associated with the Dirac operators. For their invertibility for large values of the parameter, and for the a priori estimates of solutions to associated transmission problems an analogue of Lopatinsky conditions is introduced. Finally, the Fredholm properties and the essential spectrum of transmission problems associated with the Dirac operators with singular potentials with supports on compact surfaces and non-compact surfaces with conical exits to infinity are investigated.
Reviewer: David Kapanadze (Tbilisi)Uniform regularity for a density-dependent incompressible Hall-MHD systemhttps://zbmath.org/1491.353352022-09-13T20:28:31.338867Z"Fan, Jishan"https://zbmath.org/authors/?q=ai:fan.jishan"Zhou, Yong"https://zbmath.org/authors/?q=ai:zhou.yong.1Summary: This paper proves uniform regularity for a density-dependent incompressible Hall-MHD system with positive density.Convergence towards the Vlasov-Poisson equation from the \(N\)-fermionic Schrödinger equationhttps://zbmath.org/1491.353542022-09-13T20:28:31.338867Z"Chen, Li"https://zbmath.org/authors/?q=ai:chen.li.1"Lee, Jinyeop"https://zbmath.org/authors/?q=ai:lee.jinyeop"Liew, Matthew"https://zbmath.org/authors/?q=ai:liew.matthewSummary: We consider the quantum dynamics of \(N\) interacting fermions in the large \(N\) limit. The particles in the system interact with each other via repulsive interaction that is regularized Coulomb potential with a polynomial cutoff with respect to \(N\). From the quantum system, we derive the Vlasov-Poisson system by simultaneously estimating the semiclassical and mean-field residues in terms of the Husimi measure.Anisotropic liquid drop modelshttps://zbmath.org/1491.353552022-09-13T20:28:31.338867Z"Choksi, Rustum"https://zbmath.org/authors/?q=ai:choksi.rustum"Neumayer, Robin"https://zbmath.org/authors/?q=ai:neumayer.robin"Topaloglu, Ihsan"https://zbmath.org/authors/?q=ai:topaloglu.ihsanSummary: We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotropic. In sharp contrast, Wulff shapes are the unique minimizers for certain crystalline surface tensions. We also introduce and study several related liquid drop models with anisotropic repulsion for which the Wulff shape is the minimizer in the small mass regime.Perturbations of the Landau Hamiltonian: asymptotics of eigenvalue clustershttps://zbmath.org/1491.353592022-09-13T20:28:31.338867Z"Hernandez-Duenas, G."https://zbmath.org/authors/?q=ai:hernandez-duenas.gerardo"Pérez-Esteva, S."https://zbmath.org/authors/?q=ai:perez-esteva.salvador"Uribe, A."https://zbmath.org/authors/?q=ai:uribe.alejandro"Villegas-Blas, C."https://zbmath.org/authors/?q=ai:villegas-blas.carlosSummary: We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a short-range continuous potential. The spectrum of the operator forms eigenvalue clusters. We obtain a Szegő limit theorem for the eigenvalues in the clusters as the cluster index and the field strength \(B\) tend to infinity with a fixed ratio \(\mathcal{E}\). The answer involves the averages of the potential over circles of radius \(\sqrt{\mathcal{E}/2}\) (classical orbits). After rescaling, this becomes a semiclassical problem where the role of Planck's constant is played by \(2/B\). We also discuss a related inverse spectral result.Tightness of the solutions to approximating equations of the stochastic quantization equation associated with the weighted exponential quantum field model on the two-dimensional torushttps://zbmath.org/1491.353602022-09-13T20:28:31.338867Z"Hoshino, Masato"https://zbmath.org/authors/?q=ai:hoshino.masato"Kawabi, Hiroshi"https://zbmath.org/authors/?q=ai:kawabi.hiroshi"Kusuoka, Seiichiro"https://zbmath.org/authors/?q=ai:kusuoka.seiichiro-kusuokaSummary: We consider stochastic quantization associated with the weighted exponential quantum field model on the two-dimensional torus via a method of singular stochastic partial differential equations and show the tightness of the solutions to approximating equations of the stochastic quantization equation. If the model is not weighted, then the drift term of the stochastic quantization equation, which includes a renormalization term, is nonpositive or nonnegative. However, in the weighted case, generally the drift term is neither nonpositive nor nonnegative. We modify the argument in the case without weights and discuss the weighted model.
For the entire collection see [Zbl 1482.60003].How Lagrangian states evolve into random waveshttps://zbmath.org/1491.353612022-09-13T20:28:31.338867Z"Ingremeau, Maxime"https://zbmath.org/authors/?q=ai:ingremeau.maxime"Rivera, Alejandro"https://zbmath.org/authors/?q=ai:rivera.alejandroSummary: In this paper, we consider a compact connected manifold \((X,g)\) of negative curvature, and a family of semi-classical Lagrangian states \(f_h(x)=a(x)e^{i\phi (x)/h}\) on \(X\). For a wide family of phases \(\phi \), we show that \(f_h\), when evolved by the semi-classical Schrödinger equation during a long time, resembles a random Gaussian field. This can be seen as an analogue of Berry's random waves conjecture for Lagrangian states.Global solution to the cubic Dirac equation in two space dimensionshttps://zbmath.org/1491.353732022-09-13T20:28:31.338867Z"Dong, Shijie"https://zbmath.org/authors/?q=ai:dong.shijie"Li, Kuijie"https://zbmath.org/authors/?q=ai:li.kuijieSummary: We are interested in the cubic Dirac equation with mass \(m \in [0, 1]\) in two space dimensions, which is also known as the Soler model. We conduct a thorough study on this model with initial data sufficiently small in high regularity Sobolev spaces. First, we show the global existence of the cubic Dirac equation, which is uniform-in-mass in the sense that the smallness condition on the initial data is independent of the mass parameter \(m\). In addition, we derive a unified pointwise decay result valid for all \(m \in [0, 1]\). Last but not least, we prove solution to the cubic Dirac equation scatters linearly. When the mass \(m = 0\), we can show an improved pointwise decay result.Hardy uncertainty principle for the linear Schrödinger equation on regular quantum treeshttps://zbmath.org/1491.353752022-09-13T20:28:31.338867Z"Fernández Bertolin, Aingeru"https://zbmath.org/authors/?q=ai:fernandez-bertolin.aingeru"Grecu, Andreea"https://zbmath.org/authors/?q=ai:grecu.andreea"Ignat, Liviu I."https://zbmath.org/authors/?q=ai:ignat.liviu-iSummary: In this paper we consider the linear Schrödinger equation (LSE) on a regular tree with the last generation of edges of infinite length and analyze some unique continuation properties. The first part of the paper deals with the LSE on the real line with a piece-wise constant coefficient and uses this result in the context of regular trees. The second part treats the case of a LSE with a real potential in the framework of a star-shaped graph.Global in time self-interacting Dirac fields in the de Sitter spacehttps://zbmath.org/1491.353782022-09-13T20:28:31.338867Z"Yagdjian, Karen"https://zbmath.org/authors/?q=ai:yagdjian.karenSummary: In this paper the semilinear equation of the spin-\(\frac{1}{2}\) fields in the de Sitter space is investigated. We prove the existence of the global in time small data solution in the expanding de Sitter universe. Then, under the Lochak-Majorana condition, we prove the existence of the global in time solution with large data. The sufficient conditions for the solutions to blow up in finite time are given for large data in the expanding and contracting de Sitter spacetimes. The influence of the Hubble constant on the lifespan is estimated.Ground states for Dirac equation with singular potential and asymptotically periodic conditionhttps://zbmath.org/1491.353792022-09-13T20:28:31.338867Z"Yang, Gang"https://zbmath.org/authors/?q=ai:yang.gang"Zhang, Jian"https://zbmath.org/authors/?q=ai:zhang.jian|zhang.jian.4|zhang.jian.2|zhang.jian.5|zhang.jian.1|zhang.jian.7|zhang.jian.6|zhang.jian.3Summary: In this paper we study the existence and asymptotic analysis of ground states for nonlinear Dirac equation with singular potential. Under the asymptotically periodic condition, using variational tools from non-Nehari manifold method, we establish a global compactness result and we prove that the existence of ground state solution and the continuous dependence of ground state energy about parameter as well as the asymptotic convergence of solutions.Classical approximation of a linearized three waves kinetic equationhttps://zbmath.org/1491.353822022-09-13T20:28:31.338867Z"Escobedo, M."https://zbmath.org/authors/?q=ai:escobedo.miguel|escobedo.miguel-angelSummary: The purpose of this work is to solve the Cauchy problem for the classical approximation of an isotropic linearized three waves kinetic equation that appears in the kinetic theory of a condensed gas of bosons near the critical temperature. The fundamental solution is obtained, it is proved to be unique in a suitable space of distributions, and some of its regularity and integrability properties are described. The initial value problem for integrable and locally bounded initial data is then solved. Classical solutions are obtained as functions, whose regularity depends on time and that satisfy the expected conservation of energy.Branching formula for \(q\)-Toda functions of type Bhttps://zbmath.org/1491.370592022-09-13T20:28:31.338867Z"Hoshino, Ayumu"https://zbmath.org/authors/?q=ai:hoshino.ayumu"Ohkubo, Yusuke"https://zbmath.org/authors/?q=ai:ohkubo.yusuke"Shiraishi, Jun'ichi"https://zbmath.org/authors/?q=ai:shiraishi.junichiSummary: We present a proof of the explicit formula for the asymptotically free eigenfunctions of the \(B_N \; q\)-Toda operator which was conjectured by the first and third authors [SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 084, 28 p. (2020; Zbl 1455.33010)]. This formula can be regarded as a branching formula from the \(B_N \; q\)-Toda eigenfunction restricted to the \(A_{N-1}\; q\)-Toda eigenfunctions. The proof is given by a contiguity relation of the \(A_{N-1}\; q\)-Toda eigenfunctions and a recursion relation of the branching coefficients.An amenability-like property of finite energy path and loop groupshttps://zbmath.org/1491.430022022-09-13T20:28:31.338867Z"Pestov, Vladimir"https://zbmath.org/authors/?q=ai:pestov.vladimir-gBy [\textit{P. de la Harpe}, Lect. Notes Math. 725, 220--227 (1979; Zbl 0402.46037)], a topological group \(G\) is called amenable if every continuous action of \(G\) on a compact space admits an invariant regular Borel probability measure. Equivalently, the space \(RUCB(G)\) of bounded right uniformly continuous functions on \(G\) admits a left-invariant mean. Also, in the paper under review, according to a suggestion by Martin Schneider, the authors call a topological group \(G\) admitting a left-invariant mean on the space \(LUCB(G)\), skew-amenable. In [\textit{A.~Carey} and \textit{H.~Grundling}, Lett. Math. Phys. 68, No.~2, 113--120 (2004; Zbl 1079.43003], the question is raised that if for a compact Riemannian manifold \(X\), the groups \(C^k (X,\mathrm{SU}(n)),\) \(C^\infty(X,\mathrm{SU}(n)),\) and \(H^k (X,\mathrm{SU}(n))\) with their natural group topologies are amenable. Also, there is an example of the group of gauge transformations (\(C_0 (I,\mathrm{SU}(n)\)) with the relative weak topology, where \(I = [0, 1]\)) which is not only amenable, but skew-amenable as well.
By considering the above open question, and the mentioned example, the paper under review aims to study groups of finite energy paths and loops (those of Sobolev class \(H^1 = W^1_ 2\), strictly intermediate between \(C^ 0\) and \(C^1\)). Indeed, as a main result, the authors show that for a compact connected Lie group \(K\), the topological groups of finite energy paths \(H^1 (I,K),\) loops \(H^1 (S^1 ,K),\) based paths \(H^1_0 (I,K) \), and based loops \(H^1_0 (S^1 ,K),\) as well as their central extensions, admit a left-invariant mean on the space of left uniformly continuous bounded functions. Also, the authors raise the following question that if for a compact Lie group \(K\), and a principal smooth $K$-fibre bundle \(P\), the groups of vertical automorphisms of \(P\) of classes \(C^k\), \(H^k\), \(k \geq 0,\) and \(C^\infty\) with the corresponding topologies are skew-amenable.
Reviewer: Maedeh Soroushmehr (Tehran)The physics and mathematics of Elliott Lieb. The 90th anniversary. Volume Ihttps://zbmath.org/1491.460022022-09-13T20:28:31.338867ZPublisher's description: These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry.
Around 50 chapters give an extensive account of Lieb's impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry.
A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants.
The articles of this volume will be reviewed individually.
For Volume II see [Zbl 1491.46003].
Indexed articles:
\textit{Affleck, Ian}, The Affleck-Kennedy-Lieb-Tasaki (AKLT) model, 1-6 [Zbl 07571325]
\textit{Ashbaugh, Mark S.}, On Lieb's ``On the lowest eigenvalue of the Laplacian for the intersection of two domains'', 7-17 [Zbl 07571326]
\textit{Bach, Volker}, Hartree-Fock theory, Lieb's variational principle, and their generalizations, 19-65 [Zbl 07571327]
\textit{Benguria, Rafael D.; Tubino, Trinidad}, Analytic bound on the excess charge for the Hartree model, 67-76 [Zbl 07571328]
\textit{Björnberg, Jakob E.; Ueltschi, Daniel}, Reflection positivity and infrared bounds for quantum spin systems, 77-108 [Zbl 07571329]
\textit{Breteaux, Sébastien; Faupin, Jérémy; Lemm, Marius; Sigal, Israel Michael}, Maximal speed of propagation in open quantum systems, 109-130 [Zbl 07571330]
\textit{Burke, Kieron}, Lieb's most useful contribution to density functional theory?, 131-142 [Zbl 07571331]
\textit{Carlen, Eric A.}, On some convexity and monotonicity inequalities of Elliott Lieb, 143-209 [Zbl 07571332]
\textit{Chen, Po-Ning; Wang, Mu-Tao; Wang, Ye-Kai; Yau, Shing-Tung}, Conserved quantities in general relativity -- the view from null infinity, 211-224 [Zbl 07571333]
\textit{Cheneau, Marc}, Experimental tests of Lieb-Robinson bounds, 225-245 [Zbl 07571334]
\textit{Dolbeault, Jean; Esteban, Maria J.}, Hardy-Littlewood-Sobolev and related inequalities: stability, 247-268 [Zbl 07571335]
\textit{Fermi, Davide; Giuliani, Alessandro}, Periodic striped states in Ising models with dipolar interactions, 269-293 [Zbl 07571336]
\textit{Fournais, Søren}, Atoms in strong magnetic fields, 295-314 [Zbl 07571337]
\textit{Fournais, Søren; Helffer, Bernard; Kachmar, Ayman}, Tunneling effect induced by a curved magnetic edge, 315-350 [Zbl 07571338]
\textit{Frank, Rupert L.}, Rearrangement methods in the work of Elliott Lieb, 351-375 [Zbl 07571339]
\textit{Freericks, James K.}, Quantum number towers for the Hubbard and Holstein models, 377-399 [Zbl 07571340]
\textit{Fröhlich, Jürg}, Irreversibility and the arrow of time, 401-435 [Zbl 07571341]
\textit{Griesemer, Marcel}, Ground states of atoms and molecules in non-relativistic QED, 437-450 [Zbl 07571342]
\textit{Guadagni, Gianluca; Thomas, Lawrence E.}, Perturbation theory for a non-equilibrium stationary state of a one-dimensional stochastic wave equation, 451-471 [Zbl 07571343]
\textit{Hanson, Eric Patrick; Datta, Nilanjana}, Entropies, majorization flow, and continuity bounds, 473-514 [Zbl 07571344]
\textit{Hastings, Matthew B.}, On Lieb-Robinson bounds for the double bracket flow, 515-525 [Zbl 07571345]
\textit{Helgaker, Trygve; Teale, Andrew M.}, Lieb variation principle in density-functional theory, 527-559 [Zbl 07571346]
\textit{Hepp, Klaus}, Phase transitions in Dicke models, 561-582 [Zbl 07571347]
\textit{Ilyin, Alexei; Kostianko, Anna; Zelik, Sergey}, Applications of the Lieb-Thirring and other bounds for orthonormal systems in mathematical hydrodynamics, 583-608 [Zbl 07571348]
\textit{Jauslin, Ian}, Review of a simplified approach to study the Bose gas at all densities, 609-635 [Zbl 07571349]
\textit{Kauffman, Louis H.}, Knot theory and statistical mechanics, 637-666 [Zbl 07571350]The physics and mathematics of Elliott Lieb. The 90th anniversary. Volume IIhttps://zbmath.org/1491.460032022-09-13T20:28:31.338867ZPublisher's description: These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry.
Around 50 chapters give an extensive account of Lieb's impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry.
A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants.
The articles of this volume will be reviewed individually. For Vol. I see [Zbl 1491.46002].
Indexed articles:
\textit{Langmann, Edwin}, On the construction and exact solution of the Luttinger model by Mattis and Lieb, 1-9 [Zbl 07571287]
\textit{Lebowitz, Joel L.}, Statistical mechanics of Coulomb systems: From electrons and nuclei to atoms and molecules, 11-17 [Zbl 07571288]
\textit{Lin, Fang-Hua}, Relaxed energies, defect measures, and minimal currents, 19-29 [Zbl 07571289]
\textit{Loss, Michael}, Elliott Lieb's work on stability of matter, 31-45 [Zbl 07571290]
\textit{Madrid, José}, Comparison of Ising models under change of a priori measure, 47-71 [Zbl 07571291]
\textit{Mukherjee, Chiranjib; Varadhan, Srinivasa R. S.}, The Polaron problem, 73-77 [Zbl 07571292]
\textit{Nachtergaele, Bruno}, From Lieb-Robinson bounds to automorphic equivalence, 79-92 [Zbl 07571293]
\textit{Nam, Phan Thành}, The ionization problem in quantum mechanics, 93-120 [Zbl 07571294]
\textit{Nisoli, Cristiano}, Elliott Lieb, vertex models, and artificial spin ice, 121-163 [Zbl 07571295]
\textit{Perdew, John P.; Sun, Jianwei}, The Lieb-Oxford lower bounds on the Coulomb energy, their importance to electron density functional theory, and a conjectured tight bound on exchange, 165-178 [Zbl 07571296]
\textit{Rougerie, Nicolas}, The classical Jellium and the Laughlin phase, 179-217 [Zbl 07571297]
\textit{Sabin, Julien}, Compactness methods in Lieb's work, 219-251 [Zbl 07571298]
\textit{Schimmer, Lukas}, The state of the Lieb-Thirring conjecture, 253-275 [Zbl 07571299]
\textit{Schlein, Benjamin}, Bose gases in the Gross-Pitaevskii limit: a survey of some rigorous results, 277-305 [Zbl 07571300]
\textit{Schön, Andreas; Solovej, Jan Philip}, Upper bound on the ground state energy of the two-component charged Bose gas with arbitrary masses, 307-327 [Zbl 07571301]
\textit{Schupp, Peter}, Wehrl entropy, coherent states and quantum channels, 329-344 [Zbl 07571302]
\textit{Seidl, Michael; Benyahia, Tarik; Kooi, Derk P.; Gori-Giorgi, Paola}, The Lieb-Oxford bound and the optimal transport limit of DFT, 345-360 [Zbl 07571303]
\textit{Siedentop, Heinz}, The energy and electron density of heavy atoms, 361-387 [Zbl 07571304]
\textit{Spohn, Herbert}, Recent advances on the Lieb-Liniger \(\delta\)-Bose gas, 389-404 [Zbl 07571305]
\textit{Tasaki, Hal}, The Lieb-Schultz-Mattis theorem. A topological point of view, 405-446 [Zbl 07571306]
\textit{Tian, Guang-Shan}, Lieb's spin-reflection-positivity method, Lieb lattice and all that, 447-500 [Zbl 07571307]
\textit{Wanless, Ian M.}, Lieb's permanental dominance conjecture, 501-516 [Zbl 07571308]
\textit{Yajima, Kenji}, The \(L^p\)-boundedness of wave operators for four-dimensional Schrödinger operators, 517-563 [Zbl 07571309]
\textit{Yngvason, Jakob}, A direct road to entropy and the second law of thermodynamics, 565-584 [Zbl 07571310]
\textit{Zhang, Ruixiang}, The Brascamp-Lieb inequality and its influence on Fourier analysis, 585-628 [Zbl 07571311]
\textit{Zwerger, Wilhelm}, The Lieb-Liniger gas with cold atoms, 629-652 [Zbl 07571312]Improved quantum hypercontractivity inequality for the qubit depolarizing channelhttps://zbmath.org/1491.460582022-09-13T20:28:31.338867Z"Beigi, Salman"https://zbmath.org/authors/?q=ai:beigi.salmanSummary: The hypercontractivity inequality for the qubit depolarizing channel \(\Psi_t\) states that \(\|\Psi_t^{\otimes n}(X) \|_p \leq \| X \|_q\), provided that \(p \geq q > 1\) and \(t \geq \ln \sqrt{\frac{p - 1}{q - 1}} \). In this paper, we present an improvement of this inequality. We first prove an improved quantum logarithmic-Sobolev inequality and then use the well-known equivalence of logarithmic-Sobolev inequalities and hypercontractivity inequalities to obtain our main result. As applications of these results, we present an asymptotically tight quantum Faber-Krahn inequality on the hypercube and a new quantum Schwartz-Zippel lemma.
{\copyright 2021 American Institute of Physics}Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topologyhttps://zbmath.org/1491.470332022-09-13T20:28:31.338867Z"Zagrebnov, Valentin"https://zbmath.org/authors/?q=ai:zagrebnov.valentin-aSummary: The paper improves approximation theory based on the Trotter-Kato product formulae. For self-adjoint \(C_0\)-semigroups we develop a lifting of the strongly convergent Chernoff approximation (or \textit{product}) formula to convergence in the operator-norm topology. This allows to obtain optimal estimate for the rate of operator-norm convergence of Trotter-Kato product formulae for Kato functions from the class \(K_2\).Conditions of discreteness of the spectrum for Schrödinger operator and some optimization problems for capacity and measureshttps://zbmath.org/1491.470362022-09-13T20:28:31.338867Z"Zelenko, Leonid"https://zbmath.org/authors/?q=ai:zelenko.leonidSummary: For the Schrödinger operator \(H=-\Delta+V(\mathbf{x})\cdot\), acting in the space \(L_2(\mathbb{R}^d)\) (\(d\ge 3\)), with \(V(\mathbf{x})\ge 0\) and \(V(\cdot)\in L_{1,\mathrm{loc}}(\mathbb{R}^d)\), we obtain some constructive conditions for discreteness of its spectrum. Basing on the Mazya-Shubin criterion for discreteness of the spectrum of \(H\) and using the isocapacity inequality and the concept of base polyhedron for the harmonic capacity, we have estimated from below the cost functional of an optimization problem, involved in this criterion, replacing a submodular constraint (in terms of the harmonic capacity) by a weaker but additive constraint (in terms of a measure). In this way, we obtain an optimization problem which can be considered as an infinite-dimensional analogue of the optimal covering problem. We have solved this problem for the case of a non-atomic measure. This approach enables us to obtain for the operator \(H\) some sufficient conditions for discreteness of its spectrum in terms of non-increasing rearrangements with respect to measures from the base polyhedron, for some functions connected with the potential \(V(\mathbf{x})\). We construct some counterexamples, which permit to compare our results between themselves and with results of other authors.Heavenly metrics, BPS indices and twistorshttps://zbmath.org/1491.530632022-09-13T20:28:31.338867Z"Alexandrov, Sergei"https://zbmath.org/authors/?q=ai:alexandrov.sergei-yu"Pioline, Boris"https://zbmath.org/authors/?q=ai:pioline.borisSummary: Recently, \textit{T. Bridgeland} [``Geometry from Donaldson-Thomas invariants'', Preprint, \url{arXiv:1912.06504}] defined a complex hyperkähler metric on the tangent bundle over the space of stability conditions of a triangulated category, based on a Riemann-Hilbert problem determined by the Donaldson-Thomas invariants. This metric is encoded in a function \(W(z,\theta)\) satisfying a heavenly equation, or a potential \(F(z,\theta)\) satisfying an isomonodromy equation. After recasting the RH problem into a system of TBA-type equations, we obtain integral expressions for both \(W\) and \(F\) in terms of solutions of that system. These expressions are recognized as conformal limits of the `instanton generating potential' and `contact potential' appearing in studies of D-instantons and BPS black holes. By solving the TBA equations iteratively, we reproduce Joyce's original construction of \(F\) as a formal series in the rational DT invariants. Furthermore, we produce similar solutions to deformed versions of the heavenly and isomonodromy equations involving a non-commutative star product. In the case of a finite uncoupled BPS structure, we rederive the results previously obtained by Bridgeland and obtain the so-called \(\tau\) function for arbitrary values of the fiber coordinates \(\theta\), in terms of a suitable two-variable generalization of Barnes' \(G\) function.Poly-symplectic geometry and the AKSZ formalismhttps://zbmath.org/1491.530852022-09-13T20:28:31.338867Z"Contreras, Ivan"https://zbmath.org/authors/?q=ai:contreras.ivan-a"Martínez Alba, Nicolás"https://zbmath.org/authors/?q=ai:martinez-alba.nicolasIn a previous work [J. Math. Phys. 59, No. 7, 072901, 20 p. (2018; Zbl 1430.53088)], motivated by the similarities between poly-Poisson structures and the usual Poisson structures, the authors introduced the poly-Poisson sigma model. In a nutshell, this new model is obtained by replacing the Poisson target in the Poisson sigma model by a poly-Poisson structure.
In this work, the authors consider a particular case of this general construction, namely, the case of graded manifolds and their transgression, following the AKSZ formulation. They first obtain a Schwarz-type theorem for poly-symplectic manifolds. Then they establish the existence of transgression for mapping spaces whose target is poly-symplectic. By using the transgression result, they also gives a description of the classical master equation in the poly-symplectic context.
Reviewer: Luen-Chau Li (University Park)Eigenstate thermalization hypothesis for Wigner matriceshttps://zbmath.org/1491.600112022-09-13T20:28:31.338867Z"Cipolloni, Giorgio"https://zbmath.org/authors/?q=ai:cipolloni.giorgio"Erdős, László"https://zbmath.org/authors/?q=ai:erdos.laszlo"Schröder, Dominik"https://zbmath.org/authors/?q=ai:schroder.dominikThe authors prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with high probability and with an optimal error inversely proportional to the square root of the dimension. More precisely, let $W$ be an $N\times N$ random Wigner matrix whose entries $w_{ij}$ are i.i.d. up to the symmetry constraint $w_{ij} = \overline{w_{ji}}$. Let $u_1,\ldots, u_N$ be an orthonormal eigenbasis of $W$. One of the main results of the paper states that for any deterministic matrix $A$ with $\|A\|\leq 1$ it holds that $\max_{i,j}|\langle u_i, A u_j\rangle - \delta_{ij} \mathrm{Tr}(A)/N|=\mathcal O(N^{\varepsilon-1/2})$ with very high probability. This result thus rigorously verifies the Eigenstate Thermalisation Hypothesis by \textit{J. Deutsch} [``Quantum statistical mechanics in a closed system'', Phys. Rev. A 43, No. 4, 2046--2049 (1991; \url{doi:10.1103/PhysRevA.43.2046})] for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, the authors prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in [\textit{P. Bourgade} and \textit{H. T. Yau}, Commun. Math. Phys. 350, No. 1, 231--278 (2017; Zbl 1379.58014); \textit{P. Bourgade} et al., Commun. Pure Appl. Math. 73, No. 7, 1526--1596 (2020; Zbl 1446.60005)]. On a technical level, a key contribution of this work is to identify improved multi-resolvent local laws that arise when intersplicing resolvents with traceless deterministic matrices by a careful analysis of a cumulant expansion via Feynman diagrams. The improvement also arises on the level of a single resolvent for $\mathrm{Tr}(GA)$ with $A$ traceless and deterministic, as shown in Theorem 3.
Reviewer: Marius Lemm (Cambridge)Occupation time for classical and quantum walkshttps://zbmath.org/1491.600602022-09-13T20:28:31.338867Z"Grünbaum, F. A."https://zbmath.org/authors/?q=ai:grunbaum.francisco-alberto"Velázquez, L."https://zbmath.org/authors/?q=ai:velazquez.luis"Wilkening, J."https://zbmath.org/authors/?q=ai:wilkening.jon-aFrom the Introduction: The origin of our story goes back to a remarkable observation by Paul Levy, that one dimensional Brownian motion behaves in rather unexpected ways. To state his result in everyday terms let us switch to a long night at the casino where you play repeatedly with a fair coin: if you get heads you win one dollar, if you get tails you lose one dollar. You play once every 10 s and you keep track of your ``fortune'' as a function of time: you are happy if your fortune at that time is positive, i.e., you have won more times than you have lost, otherwise you are unhappy. This game has to be played for a fixed and large number of tosses. What proportion of the total time you play do you expect to be happy? It is not unreasonable to guess that the answer should be about 1/2.
However, and this is P. Levy's observation, a ``wild night'' is more likely than a ``normal night''. Take -- for instance -- two windows of total length 1/10: then the probability that you are happy somewhere between 45 and 55\% of the time is smaller than the probability that you are happy either more than 95 or less than 5\% of the time. This discussion can be found in many standard probability books. The distribution of the random variable in question is explicitly known -- and is given by an arcsine law -- and as evidence of its interest we observe that one of the first applications of the Feynman-Kac formula was a rederivation of this result of P. Levy by \textit{M. Kac}, see [in: Proc. Berkeley Sympos. Math. Statist. Probability, California Juli 31-- August 12, 1950, 189--215 (1951; Zbl 0045.07002)]. The careful formulation of the discrete version with Brownian motion replaced by a coin was done by K. Chung and W. Feller.
Just to put things in perspective, consider two-dimensional Brownian motion starting at the origin, run it for time one and inquire about the time spent in the positive quadrant. The analytical form of the result is not known.
The rest of this paper is devoted to a discussion of what happens when one replaces a classical random walk on the integers, such as the ordinary coin, with a quantum walk.
For the entire collection see [Zbl 1479.47003].Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity. I: measureshttps://zbmath.org/1491.600952022-09-13T20:28:31.338867Z"Bringmann, Bjoern"https://zbmath.org/authors/?q=ai:bringmann.bjornThe author of this study shows the Gibbs measure invariance for a three-dimensional wave equation with a Hartree nonlinearity. The singularity of the Gibbs measure with respect to the Gaussian free field is the primary innovation. In both measure-theoretic and dynamical aspects, the singularity has various repercussions. In this study, the author primarily creates and investigates the Gibbs measure. The technique used in this research is based on previous work by Barashkov and Gubinelli for the \(\Phi^4_3\)-model. In addition, the author creates new techniques to cope with the Hartree interaction's nonlocality. Depending on the regularity of the interaction potential, the exact threshold between singularity and absolute continuity of the Gibbs measure are also calculated.
Reviewer: Udhayakumar Ramalingam (Vellore)About one method of numerical solution Schrödinger equationhttps://zbmath.org/1491.650122022-09-13T20:28:31.338867Z"Plokhotnikov, K. E."https://zbmath.org/authors/?q=ai:plokhotnikov.k-ehSummary: The paper considers the method of numerical solution of the Schrödinger equation, which, in part, can be attributed to the class of Monte Carlo methods. The method is presented and simultaneously illustrated by the examples of solving the one-dimensional and multidimensional Schrödinger equation in the problems of linear one-dimensional oscillator, hydrogen atom and benzene.Why it is sufficient to have real-valued amplitudes in quantum computinghttps://zbmath.org/1491.680742022-09-13T20:28:31.338867Z"Bautista, Isaac"https://zbmath.org/authors/?q=ai:bautista.isaac"Kreinovich, Vladik"https://zbmath.org/authors/?q=ai:kreinovich.vladik-ya"Kosheleva, Olga"https://zbmath.org/authors/?q=ai:kosheleva.olga-m"Nguyen, Hoang Phuong"https://zbmath.org/authors/?q=ai:nguyen.hoang-phuongIn this paper an arbitrary $n$-qubit state with complex amplitudes is transformed to an $(n+1)$-qubit state with real-valued amplitudes only. This idea is simple and no problem. However, for concrete quantum computing and quantum algorithms, I am not sure how this works since the present method gives just a simple transformation from a state to another state. It seems still far from realizing quantum computing and quantum algorithms without complex amplitudes.
So, I hope to further see the concrete process of realizing a general quantum algorithm, or at least some important examples of quantum algorithms should be illustrated (e.g., Shor's algorithm and Grover's algorithm).
For the entire collection see [Zbl 1470.92013].
Reviewer: Daowen Qiu (Guangzhou)Quantum online streaming algorithms with logarithmic memoryhttps://zbmath.org/1491.680752022-09-13T20:28:31.338867Z"Khadiev, Kamil"https://zbmath.org/authors/?q=ai:khadiev.kamil"Khadieva, Aliya"https://zbmath.org/authors/?q=ai:khadieva.aliyaSummary: We consider quantum and classical (deterministic or randomize) streaming online algorithms with respect to competitive ratio. We show that there is a problem that can be solved by a quantum online streaming algorithm better than by classical ones in the case of logarithmic memory. The problem is an online version of the Disjointness problem (Checking weather two sets are disjoint or not).Triggering recollisions with XUV pulses: imprint of recolliding periodic orbitshttps://zbmath.org/1491.780122022-09-13T20:28:31.338867Z"Dubois, J."https://zbmath.org/authors/?q=ai:dubois.jonathan-l|dubois.jean-luc|dubois.jean-guy|dubois.jean-emile|dubois.j-m|dubois.jerome|dubois.jacques-emile|dubois.jacques-o|dubois.jacque-octave|dubois.joel"Jorba, À."https://zbmath.org/authors/?q=ai:jorba.angelSummary: We consider an electron in an atom driven by an infrared (IR) elliptically polarized laser field after its ionization by an ultrashort extreme ultraviolet (XUV) pulse. We find that, regardless of the atom species and the laser ellipticity, there exists XUV parameters for which the electron returns to its parent ion after ionizing, i.e., undergoes a recollision. This shows that XUV pulses trigger efficiently recollisions in atoms regardless of the ellipticity of the IR field. The XUV parameters for which the electron undergoes a recollision are obtained by studying the location of recolliding periodic orbits (RPOs) in phase space. The RPOs and their linear stability are followed and analyzed as a function of the intensity and ellipticity of the IR field. We determine the relation between the RPOs identified here and the ones found in the literature and used to interpret other types of highly nonlinear phenomena for low elliptically and circularly polarized IR fields.Floquet engineering of electric polarization with two-frequency drivehttps://zbmath.org/1491.780132022-09-13T20:28:31.338867Z"Ikeda, Yuya"https://zbmath.org/authors/?q=ai:ikeda.yuya"Kitamura, Sota"https://zbmath.org/authors/?q=ai:kitamura.sota"Morimoto, Takahiro"https://zbmath.org/authors/?q=ai:morimoto.takahiroSummary: Electric polarization is a geometric phenomenon in solids and has a close relationship to the symmetry of the system. Here we propose a mechanism to dynamically induce and manipulate electric polarization by using an external light field. Specifically, we show that application of bicircular lights controls the rotational symmetry of the system and can generate electric polarization. To this end, we use Floquet theory to study a system subjected to a two-frequency drive. We derive an effective Hamiltonian with high-frequency expansions, for which the electric polarization is computed with the Berry phase formula. We demonstrate the dynamical control of polarization for a one-dimensional Su-Shrieffer-Heeger chain, a square lattice model, and a honeycomb lattice model.FXRS: fast X-ray spectrum-simulator theory and software implementationhttps://zbmath.org/1491.780172022-09-13T20:28:31.338867Z"Chirilǎ, Ciprian C."https://zbmath.org/authors/?q=ai:chirila.ciprian-c"Ha, T. M. H."https://zbmath.org/authors/?q=ai:ha.t-m-hSummary: We propose a simple, computationally efficient scheme for an X-ray spectrum simulator. The theoretical models describing the physical processes involved are employed in our Monte Carlo software in a coherent way, paving the way for straightforward future improvements. Our results compare satisfactorily to experimental results from literature and to results from dedicated simulation software. The simplicity, excellent statistical errors, and short execution time of our code recommend it for intensive use in X-ray generation simulations.Equidistribution of dynamical systems. Time-quantitative second lawhttps://zbmath.org/1491.800022022-09-13T20:28:31.338867Z"Beck, Jozsef"https://zbmath.org/authors/?q=ai:beck.jozsefPublisher's description: We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)?
Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like ``disorder'' and ``energy spreading'') into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a ``soft'' qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium.
The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox.Quantum communication, quantum networks, and quantum sensinghttps://zbmath.org/1491.810012022-09-13T20:28:31.338867Z"Djordjevic, Ivan"https://zbmath.org/authors/?q=ai:djordjevic.ivan-bPublisher's description: Quantum Communication, Quantum Networks, and Quantum Sensing represents a self-contained introduction to quantum communication, quantum error-correction, quantum networks, and quantum sensing. It starts with basic concepts from classical detection theory, information theory, and channel coding fundamentals before continuing with basic principles of quantum mechanics including state vectors, operators, density operators, measurements, and dynamics of a quantum system. It continues with fundamental principles of quantum information processing, basic quantum gates, no-cloning and theorem on indistinguishability of arbitrary quantum states. The book then focuses on quantum information theory, quantum detection and Gaussian quantum information theories, and quantum key distribution (QKD). The book then covers quantum error correction codes (QECCs) before introducing quantum networks. The book concludes with quantum sensing and quantum radars, quantum machine learning and fault-tolerant quantum error correction concepts.Modern physics. Introduction to statistical mechanics, relativity, and quantum physicshttps://zbmath.org/1491.810022022-09-13T20:28:31.338867Z"Salasnich, Luca"https://zbmath.org/authors/?q=ai:salasnich.lucaPublisher's description: This book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of ``Quantum Physics'' belonging to the Bachelor of Science in Material Sciences at the University of Padova.
The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrödinger equation, which was obtained by Erwin Schrödinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics.
The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.Invitation to quantum mechanicshttps://zbmath.org/1491.810032022-09-13T20:28:31.338867Z"Styer, Daniel F."https://zbmath.org/authors/?q=ai:styer.daniel-fPublisher's description: How do atoms and electrons behave? Are they just like marbles, basketballs, suns, and planets, but smaller?
They are not. Atoms and electrons behave in a fashion quite unlike the familiar marbles, basketballs, suns, and planets. This sophomore-level textbook delves into the counterintuitive, intricate, but ultimately fascinating world of quantum mechanics. Building both physical insight and mathematical technique, it opens up a new world to the discerning reader.
After discussing experimental demonstrations showing that atoms behave differently from marbles, the book builds up the phenomena of the quantum world -- quantization, interference, and entanglement -- in the simplest possible system, the qubit. Once the phenomena are introduced, it builds mathematical machinery for describing them. It goes on to generalize those concepts and that machinery to more intricate systems. Special attention is paid to identical particles, the source of considerable student confusion. In the last chapter, students get a taste of what is not treated in the book and are invited to continue exploring quantum mechanics. Problems in the book test both conceptual and technical knowledge, and invite students to develop their own questions.Interplay of quantum mechanics and nonlinearity. Understanding small-system dynamics of the discrete nonlinear Schrödinger equationhttps://zbmath.org/1491.810042022-09-13T20:28:31.338867Z"Kenkre, V. M. (Nitant)"https://zbmath.org/authors/?q=ai:kenkre.vasudev-mangeshPublisher's description: This book presents an in-depth study of the discrete nonlinear Schrödinger equation (DNLSE), with particular emphasis on spatially small systems that permit analytic solutions. In many quantum systems of contemporary interest, the DNLSE arises as a result of approximate descriptions despite the fundamental linearity of quantum mechanics. Such scenarios, exemplified by polaron physics and Bose-Einstein condensation, provide application areas for the theoretical tools developed in this text. The book begins with an introduction of the DNLSE illustrated with the dimer, development of fundamental analytic tools such as elliptic functions, and the resulting insights into experiment that they allow. Subsequently, the interplay of the initial quantum phase with nonlinearity is studied, leading to novel phenomena with observable implications in fields such as fluorescence depolarization of stick dimers, followed by analysis of more complex and/or larger systems. Specific examples analyzed in the book include the nondegenerate nonlinear dimer, nonlinear trapping, rotational polarons, and the nonadiabatic nonlinear dimer. Phenomena treated include strong carrier-phonon interactions and Bose-Einstein condensation. This book is aimed at researchers and advanced graduate students, with chapter summaries and problems to test the reader's understanding, along with an extensive bibliography. The book will be essential reading for researchers in condensed matter and low-temperature atomic physics, as well as any scientist who wants fascinating insights into the role of nonlinearity in quantum physics.Quantum computing for the brainhttps://zbmath.org/1491.810052022-09-13T20:28:31.338867Z"Swan, Melanie"https://zbmath.org/authors/?q=ai:swan.melanie"dos Santos, Renato P."https://zbmath.org/authors/?q=ai:dos-santos.renato-p"Lebedev, Mikhail"https://zbmath.org/authors/?q=ai:lebedev.mikhail"Witte, Frank"https://zbmath.org/authors/?q=ai:witte.frankPublisher's description: Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain.
Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in neuroscience applications such as neural signaling and synaptic integration. State-of-the-art methods are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, spiking neural networks, quantum teleportation, and quantum walks.
Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing.Mass term effect on fractional quantum Hall states of Dirac particleshttps://zbmath.org/1491.810062022-09-13T20:28:31.338867Z"Yonaga, Kouki"https://zbmath.org/authors/?q=ai:yonaga.koukiPublisher's description: This book presents the high-precision analysis of ground states and low-energy excitations in fractional quantum Hall states formed by Dirac electrons, which have attracted a great deal of attention. In particular the author focuses on the physics of fractional quantum Hall states in graphene on a hexagonal boron nitride substrate, which was recently implemented in experiments. The numerical approach employed in the book, which uses an exact numerical diagonalization of an effective model Hamiltonian on a Haldane's sphere based on pseudopotential representation of electron interaction, provides a better understanding of the recent experiments.
The book reviews various aspects of quantum Hall effect: a brief history, recent experiments with graphene, and fundamental theories on integer and fractional Hall effects. It allows readers to quickly grasp the physics of quantum Hall states of Dirac fermions, and to catch up on latest research on the quantum Hall effect in graphene.Steven Weinberg (1933-2021): Titan of theoretical physicshttps://zbmath.org/1491.810072022-09-13T20:28:31.338867Z"Preskill, John"https://zbmath.org/authors/?q=ai:preskill.john(no abstract)Coherent manipulation of an Andreev spin qubithttps://zbmath.org/1491.810082022-09-13T20:28:31.338867Z"Hays, M."https://zbmath.org/authors/?q=ai:hays.mark-h"Fatemi, V."https://zbmath.org/authors/?q=ai:fatemi.valla"Bouman, D."https://zbmath.org/authors/?q=ai:bouman.d"Cerrillo, J."https://zbmath.org/authors/?q=ai:cerrillo.javier"Diamond, S."https://zbmath.org/authors/?q=ai:diamond.solomon-gilbert|diamond.sandra-l|diamond.scott-l|diamond.steven"Serniak, K."https://zbmath.org/authors/?q=ai:serniak.k"Connolly, T."https://zbmath.org/authors/?q=ai:connolly.thomas-m|connolly.t-john|connolly.thomas-h|connolly.terry|connolly.thomas-j"Krogstrup, P."https://zbmath.org/authors/?q=ai:krogstrup.peter"Nygård, J."https://zbmath.org/authors/?q=ai:nygard.jan-f"Levy Yeyati, A."https://zbmath.org/authors/?q=ai:yeyati.a-levy"Geresdi, A."https://zbmath.org/authors/?q=ai:geresdi.a"Devoret, M. H."https://zbmath.org/authors/?q=ai:devoret.michel-h(no abstract)Coherent manipulation of a spin qubithttps://zbmath.org/1491.810092022-09-13T20:28:31.338867Z"Wendin, Göran"https://zbmath.org/authors/?q=ai:wendin.goran"Shumeiko, Vitaly"https://zbmath.org/authors/?q=ai:shumeiko.vitalyFrom the summary: Quantum computers (QCs) promise to exponentially speed up a number of problems in optimization, materials science, and chemistry. The caveat is that they may not even get the chance. One outstanding issue is the coherence time, which is how long a system can remain in a quantum state. We live in the era of noisy intermediate-scale quantum processors, and the time to execute the necessary number of gates in the quantum circuit may be longer than the coherence time of the quantum register. Extending coherence time can be accomplished by improving the properties for existing qubits, which is tedious and demands large resources but almost guarantees steady progress. Alternatively, looking for alternative qubits holds the promise of a breakthrough, if it does not end up becoming a wild goose chase.Physical models for quantum dotshttps://zbmath.org/1491.810102022-09-13T20:28:31.338867ZPublisher's description: Since the early 1990s, quantum dots have become an integral part of research in solid state physics for their fundamental properties that mimic the behavior of atoms and molecules on a larger scale. They also have a broad range of applications in engineering and medicines for their ability to tune their electronic properties to achieve specific functions. This book is a compilation of articles that span 20 years of research on comprehensive physical models developed by their authors to understand the detailed properties of these quantum objects and to tailor them for specific applications. Far from being exhaustive, this book focuses on topics of interest for solid state physicists, materials scientists, engineers, and general readers, such as quantum dots and nanocrystals for single-electron charging with applications in memory devices, quantum dots for electron-spin manipulation with applications in quantum information processing, and finally self-assembled quantum dots for applications in nanophotonics.
The articles of this volume will not be indexed individually.17th conference on the theory of quantum computation, communication and cryptography, TQC 2022, Urbana Champaign, Illinois, USA, July 11--15, 2022https://zbmath.org/1491.810112022-09-13T20:28:31.338867ZThe articles of this volume will be reviewed individually. For the preceding conference see [Zbl 1465.81007].Convergent iteration in Sobolev space for time dependent closed quantum systemshttps://zbmath.org/1491.810122022-09-13T20:28:31.338867Z"Jerome, Joseph W."https://zbmath.org/authors/?q=ai:jerome.joseph-wSummary: Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via iterative methods in Sobolev space based upon evolution operators. Recently, existence and uniqueness of weak solutions were demonstrated by a contractive fixed point mapping defined by the evolution operators. Convergent successive approximation is then guaranteed. This article uses the same mapping to define quadratically convergent Newton and approximate Newton methods. Estimates for the constants used in the convergence estimates are provided. The evolution operators are ideally suited to serve as the framework for this operator approximation theory, since the Hamiltonian is time-dependent. In addition, the hypotheses required to guarantee quadratic convergence of the Newton iteration build naturally upon the hypotheses used for the existence/uniqueness theory.Quantum mechanics-free subsystem with mechanical oscillatorshttps://zbmath.org/1491.810132022-09-13T20:28:31.338867Z"de Lépinay, Laure Mercier"https://zbmath.org/authors/?q=ai:de-lepinay.laure-mercier"Ockeloen-Korppi, Caspar F."https://zbmath.org/authors/?q=ai:ockeloen-korppi.caspar-f"Woolley, Matthew J."https://zbmath.org/authors/?q=ai:woolley.matthew-james"Sillanpää, Mika A."https://zbmath.org/authors/?q=ai:sillanpaa.mika-aSummary: Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics -- free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.The Internet goes quantumhttps://zbmath.org/1491.810142022-09-13T20:28:31.338867Z"Popkin, Gabriel"https://zbmath.org/authors/?q=ai:popkin.gabriel(no abstract)Programming a quantum phase of matterhttps://zbmath.org/1491.810152022-09-13T20:28:31.338867Z"Bartlett, Stephen D."https://zbmath.org/authors/?q=ai:bartlett.stephen-dSummary: From the abstract: At very low temperatures, some materials may condense into exotic phases of matter, where quantum entanglement becomes the dominant feature governing their behavior. These quantum phases -- a world different from the ordinary states of solid, liquid, gas, and plasma -- exhibit exotic properties such as quasiparticle excitations that interfere with each other in unusual ways. From an application point of view, these quantum phases may serve a key role in increasing the robustness of quantum memory devices -- a key component in quantum computers. However, although theorists have predicted the existence of these quantum phases under a variety of conditions, quantum phases with long-range entanglement are extremely difficult to realize experimentally.Semi-quantum moneyhttps://zbmath.org/1491.810162022-09-13T20:28:31.338867Z"Radian, Roy"https://zbmath.org/authors/?q=ai:radian.roy"Sattath, Or"https://zbmath.org/authors/?q=ai:sattath.orSummary: Quantum money allows a bank to mint quantum money states that can later be verified and cannot be forged. Usually, this requires a quantum communication infrastructure to perform transactions. \textit{D. Gavinsky} [``Quantum money with classical verification'', in: Proceedings of the 2012 IEEE 27th annual conference on computational complexity, CCC 2012, Porto, Portugal, June 26--29, 2012. Los Alamitos, CA: IEEE Computer Society. 42--52 (2012; \url{doi:10.1109/CCC.2012.10})] introduced the notion of classically verifiable quantum money, which allows verification through classical communication. In this work, we introduce the notion of classical minting and combine it with classical verification to introduce semi-quantum money. Semi-quantum money is the first type of quantum money to allow transactions with completely classical communication and an entirely classical bank. This work features constructions for both a public memory-dependent semi-quantum money scheme and a private memoryless semi-quantum money scheme. The public construction is based on the works of Zhandry and Coladangelo, and the private construction is based on the notion of noisy trapdoor claw-free functions (NTCF) introduced by \textit{Z. Brakerski} et al. [``A cryptographic test of quantumness and certifiable randomness from a single quantum device'', in: Proceedings of the 59th annual IEEE symposium on foundations of computer science, FOCS 2018, Paris, France, October 7--9, 2018. Los Alamitos, CA: IEEE Computer Society. 320--331 (2018; \url{doi:10.1109/FOCS.2018.00038})]. In terms of technique, our main contribution is a perfect parallel repetition theorem for NTCF.Anderson localisation for infinitely many interacting particles in Hartree-Fock theoryhttps://zbmath.org/1491.810172022-09-13T20:28:31.338867Z"Ducatez, Raphael"https://zbmath.org/authors/?q=ai:ducatez.raphaelSummary: We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice and that they are submitted to an external periodic potential which creates a gap in the non-interacting one particle Hamiltonian. We also assume that the interaction is weak enough to preserve a gap. We prove that the mean-field operator has exponentially localised eigenvectors, either on its whole spectrum or at the edges of its bands, depending on the strength of the disorder.Two-particle bound states at interfaces and cornershttps://zbmath.org/1491.810182022-09-13T20:28:31.338867Z"Roos, Barbara"https://zbmath.org/authors/?q=ai:roos.barbara"Seiringer, Robert"https://zbmath.org/authors/?q=ai:seiringer.robertSummary: We study two interacting quantum particles forming a bound state in \(d\)-dimensional free space, and constrain the particles in \(k\) directions to \(( 0 , \infty )^k \times \mathbb{R}^{d - k} \), with Neumann boundary conditions. First, we prove that the ground state energy strictly decreases upon going from \(k\) to \(k + 1\). This shows that the particles stick to the corner where all boundary planes intersect. Second, we show that for all \(k\) the resulting Hamiltonian, after removing the free part of the kinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper generalizes the work of \textit{S. Egger} et al. [J. Spectr. Theory 10, No. 4, 1413--1444 (2020; Zbl 1469.81021)] to dimensions \(d > 1\).Geometric squeezing into the lowest Landau levelhttps://zbmath.org/1491.810192022-09-13T20:28:31.338867Z"Fletcher, Richard J."https://zbmath.org/authors/?q=ai:fletcher.richard-j"Shaffer, Airlia"https://zbmath.org/authors/?q=ai:shaffer.airlia"Wilson, Cedric C."https://zbmath.org/authors/?q=ai:wilson.cedric-c"Patel, Parth B."https://zbmath.org/authors/?q=ai:patel.parth-b"Yan, Zhenjie"https://zbmath.org/authors/?q=ai:yan.zhenjie"Crépel, Valentin"https://zbmath.org/authors/?q=ai:crepel.valentin"Mukherjee, Biswaroop"https://zbmath.org/authors/?q=ai:mukherjee.biswaroop"Zwierlein, Martin W."https://zbmath.org/authors/?q=ai:zwierlein.martin-wSummary: The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits' centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.Controlling quantum many-body dynamics in driven Rydberg atom arrayshttps://zbmath.org/1491.810202022-09-13T20:28:31.338867Z"Bluvstein, Dolev"https://zbmath.org/authors/?q=ai:bluvstein.dolev"Omran, Ahmed"https://zbmath.org/authors/?q=ai:omran.ahmed-abed-ali"Levine, Harry"https://zbmath.org/authors/?q=ai:levine.harry"Keesling, Alexander"https://zbmath.org/authors/?q=ai:keesling.alexander"Semeghini, Giulia"https://zbmath.org/authors/?q=ai:semeghini.giulia"Ebadi, Sepehr"https://zbmath.org/authors/?q=ai:ebadi.sepehr"Wang, Tout T."https://zbmath.org/authors/?q=ai:wang.tout-t"Michailidis, Alexios A."https://zbmath.org/authors/?q=ai:michailidis.alexios-a"Maskara, Nishad"https://zbmath.org/authors/?q=ai:maskara.nishad"Ho, Wen Wei"https://zbmath.org/authors/?q=ai:ho.wen-wei"Choi, Soonwon"https://zbmath.org/authors/?q=ai:choi.soonwon"Serbyn, Maksym"https://zbmath.org/authors/?q=ai:serbyn.maksym"Greiner, Markus"https://zbmath.org/authors/?q=ai:greiner.markus"Vuletic, Vladan"https://zbmath.org/authors/?q=ai:vuletic.vladan"Lukin, Mikhail D."https://zbmath.org/authors/?q=ai:lukin.mikhail-dSummary: The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.Restriction for general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case)https://zbmath.org/1491.810212022-09-13T20:28:31.338867Z"Chan, Kei Yuen"https://zbmath.org/authors/?q=ai:chan.kei-yuenSummary: We prove a local Gan-Gross-Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier-Jacobi models and study a possible generalization to Ext-branching laws.Supercoherent states, group-geometrical realizations and simplest supergroupshttps://zbmath.org/1491.810222022-09-13T20:28:31.338867Z"Cirilo-Lombardo, Diego Julio"https://zbmath.org/authors/?q=ai:cirilo-lombardo.diego-julioSummary: Explicit construction of supercoherent states (SCS) of the Klauder-Perelomov type which were used as structural basis of the electroweak sector of the standard model (SM) in [\textit{A. B. Arbuzov} and \textit{D. J. Cirilo-Lombardo}, ``Dynamical breaking of symmetries beyond the standard model and supergeometry'', Phys. Scr. 94, No. 12, Article ID 125302, 24 p. (2019; \url{doi:10.1088/1402-4896/ab35f6})] is presented taking into account the geometry of the coset based in the simplest supergroup \(SU\left( 2\mid 1\right) \): the technical details is the focus of this work. The constructed coherent superstates uses group representation from \textit{Y. Neíeman} et al. [``Superconnections for electroweak su(2/1) and extensions, and the mass of the Higgs'', Phys. Rept. 406, No. 5, 303--377 (2005; \url{doi:10.1016/j.physrep.2004.10.005})] for a beyond SM, however not only the even part of the supergroup works as the embedding for the electroweak sector of SM, but the supercoherent states into the model are capable to introduce a hidden sector.A Poisson algebra on the Hida test functions and a quantization using the Cuntz algebrahttps://zbmath.org/1491.810232022-09-13T20:28:31.338867Z"Bock, Wolfgang"https://zbmath.org/authors/?q=ai:bock.wolfgang"Futorny, Vyacheslav"https://zbmath.org/authors/?q=ai:futorny.vyacheslav-m"Neklyudov, Mikhail"https://zbmath.org/authors/?q=ai:neklyudov.mikhailSummary: In this note, we define one more way of quantization of classical systems. The quantization we consider is an analogue of classical Jordan-Schwinger map which has been known and used for a long time by physicists. The difference, compared to Jordan-Schwinger map, is that we use generators of Cuntz algebra \(\mathcal{O}_{\infty}\) (i.e. countable family of mutually orthogonal partial isometries of separable Hilbert space) as a ``building blocks'' instead of creation-annihilation operators. The resulting scheme satisfies properties similar to Van Hove prequantization, i.e. exact conservation of Lie brackets and linearity.String breaking in a cold wind as seen by string modelshttps://zbmath.org/1491.810242022-09-13T20:28:31.338867Z"Andreev, Oleg"https://zbmath.org/authors/?q=ai:andreev.oleg-dmitrievich|andreev.oleg-aSummary: Using the gauge/string duality, we model a heavy quark-antiquark pair in a color singlet state moving through a cold medium and explore the consequences of temperature and velocity on string breaking. In doing so, we restrict to the case of two dynamical flavors. We show that the string breaking distance slowly varies with temperature and velocity away from the critical line but could fall near it.FZZ-triality and large \(\mathcal{N} = 4\) super Liouville theoryhttps://zbmath.org/1491.810252022-09-13T20:28:31.338867Z"Creutzig, Thomas"https://zbmath.org/authors/?q=ai:creutzig.thomas"Hikida, Yasuaki"https://zbmath.org/authors/?q=ai:hikida.yasuakiSummary: We examine dualities of two dimensional conformal field theories by applying the methods developed by the authors. We first derive the duality between \(SL(2|1)_k/(SL(2)_k \otimes U(1))\) coset and Witten's cigar model or sine-Liouville theory. The latter two models are Fateev-Zamolodchikov-Zamolodchikov (FZZ-)dual to each other, hence the relation of the three models is named FZZ-triality. These results are used to study correlator correspondences between large \(\mathcal{N} = 4\) super Liouville theory and a coset of the form \(Y(k_1, k_2)/SL(2)_{k_1 + k_2}\), where \(Y(k_1, k_2)\) consists of two \(SL(2|1)_{k_i}\) and free bosons or equivalently two \(U(1)\) cosets of \(D(2, 1; k_i - 1)\) at level one. These correspondences are a main result of this paper. The FZZ-triality acts as a seed of the correspondence, which in particular implies a hidden \(SL(2)_{k^\prime}\) in \(SL(2|1)_k\) or \(D(2, 1; k - 1)_1\). The relation of levels is \(k^\prime - 1 = 1/(k-1)\). We also construct boundary actions in sine-Liouville theory as another use of the FZZ-triality. Furthermore, we generalize the FZZ-triality to the case with \(SL(n|1)_k /(SL(n)_k \otimes U(1))\) for arbitrary \(n > 2\).Minimal gauge invariant couplings at order \(\ell_p^6\) in M-theoryhttps://zbmath.org/1491.810262022-09-13T20:28:31.338867Z"Garousi, Mohammad R."https://zbmath.org/authors/?q=ai:garousi.mohammad-rSummary: Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of the gauge invariant couplings at order \(\ell_p^6\) for the bosonic fields of M-theory, we have found that the minimum number of independent couplings in the structures with even number of the three-form, is 1062. We find that there are schemes in which there is no coupling involving \(R\), \(R_{\mu\nu}\), \(\nabla_\mu F^{\mu\alpha\beta\gamma}\). In these schemes, there are sub-schemes in which, except one coupling which has the second derivative of \(F^{(4)}\), the couplings can have no term with more than two derivatives. We find some of the parameters by dimensionally reducing the couplings on a circle and comparing them with the known couplings of the one-loop effective action of type IIA superstring theory. In particular, we find the coupling which has term with more than two derivatives is zero.Using a nested anomaly detection machine learning algorithm to study the neutral triple gauge couplings at an \(e^+e^-\) colliderhttps://zbmath.org/1491.810272022-09-13T20:28:31.338867Z"Yang, Ji-Chong"https://zbmath.org/authors/?q=ai:yang.ji-chong"Guo, Yu-Chen"https://zbmath.org/authors/?q=ai:guo.yuchen"Cai, Li-Hua"https://zbmath.org/authors/?q=ai:cai.li-huaSummary: Anomaly detection algorithms have been proved to be useful in the search of new physics beyond the Standard Model. However, a prerequisite for using an anomaly detection algorithm is that the signal to be sought is indeed anomalous. This does not always hold true, for example when interference between new physics and the Standard Model becomes important. In this case, the search of new physics is no longer an anomaly detection. To overcome this difficulty, we propose a nested anomaly detection algorithm, which appears to be useful in the study of neutral triple gauge couplings at the CEPC, the ILC and the FCC-ee. Our approach inherits the advantages of the anomaly detection algorithm been nested, while at the same time, it is no longer an anomaly detection algorithm. As a complement to anomaly detection algorithms, it can achieve better results on problems that are no longer anomaly detection.Constraining light mediators via detection of coherent elastic solar neutrino nucleus scatteringhttps://zbmath.org/1491.810282022-09-13T20:28:31.338867Z"Li, Yu-Feng"https://zbmath.org/authors/?q=ai:li.yufeng|li.yu-feng"Xia, Shuo-yu"https://zbmath.org/authors/?q=ai:xia.shuo-yuSummary: Dark matter (DM) direct detection experiments are entering the multiple-ton era and will be sensitive to the coherent elastic neutrino nucleus scattering (CE\(\nu\)NS) of solar neutrinos, enabling the possibility to explore contributions from new physics with light mediators at the low energy range. In this paper we consider light mediator models (scalar, vector and axial vector) and the corresponding contributions to the solar neutrino CE\(\nu\)NS process. Motivated by the current status of new generation of DM direct detection experiments and the future plan, we study the sensitivity of light mediators in DM direct detection experiments of different nuclear targets and detector techniques. The constraints from the latest \(^8\mathrm{B}\) solar neutrino measurements of XENON-1T are also derived. Finally, we show that the solar neutrino CE\(\nu\)NS process can provide stringent limitation on the \(L_\mu - L_\tau\) model with the vector mediator mass below 100 MeV, covering the viable parameter space of the solution to the \((g - 2)_\mu\) anomaly.Pion form factor from an AdS deformed backgroundhttps://zbmath.org/1491.810292022-09-13T20:28:31.338867Z"Martín Contreras, Miguel Angel"https://zbmath.org/authors/?q=ai:martin-contreras.miguel-angel"Capossoli, Eduardo Folco"https://zbmath.org/authors/?q=ai:capossoli.eduardo-folco"Li, Danning"https://zbmath.org/authors/?q=ai:li.danning"Vega, Alfredo"https://zbmath.org/authors/?q=ai:vega.alfredo"Boschi-Filho, Henrique"https://zbmath.org/authors/?q=ai:boschi-filho.henriqueSummary: We consider a bottom-up AdS/QCD model with a conformal exponential deformation \(e^{k_I z^2}\) on a Lorentz invariant AdS background, where \(k_I\) stands for the scale \(k_\pi\) that fixes confinement in the pion case and \(k_\gamma\) for the kinematical energy scale associated with the virtual photon. In this model we assume the conformal dimension associated with the operator that creates pions at the boundary as \(\Delta = 3\), as in the original bottom-up AdS/QCD proposals. Regarding the geometric slope related to photon field \(k_\gamma\), we analyze two cases: constant and depending on the transferred momentum \(q\). In these two cases we computed the electromagnetic pion form factor as well as the pion radius. We compare our results with experimental data as well as other theoretical (holographic and non-holographic) models. In particular, for the momentum dependent scale, we find good agreement with the available experimental data as well as non-holographic models.The 28 GeV dimuon excess in lepton specific THDMhttps://zbmath.org/1491.810302022-09-13T20:28:31.338867Z"Çiçi, Ali"https://zbmath.org/authors/?q=ai:cici.ali"Khalil, Shaaban"https://zbmath.org/authors/?q=ai:khalil.shaaban"Niş, Büşra"https://zbmath.org/authors/?q=ai:nis.busra"Ün, Cem Salih"https://zbmath.org/authors/?q=ai:un.cem-salihSummary: We explore the Higgs mass spectrum in a class of Two Higgs Doublet Models (THDMs) in which a scalar \(SU(2)_L\) doublet interacts only with quarks, while the second one interacts only with leptons. The spectrum includes two CP-even Higgs bosons, either of which can account for the SM-like Higgs boson, and the spectra involving light Higgs bosons receive strong impacts from the LEP results and the current collider analyses. We find that a consistent spectrum can involve a CP-odd Higgs boson as light as about 10 GeV, while the lightest CP-even Higgs boson cannot be lighter than about 55 GeV when \(m_A \sim 28\) GeV. These analyses can rather bound the low \(\tan\beta\) region which can also accommodate an observed excess in dimuon events at \(m_{\mu\mu} \sim 28\) GeV. A lepton-specific class of THDMs (LS-THDM) can predict such an excess through \(A \to \mu\mu\) decays, while the solutions can be constrained by the \(A \to \tau\tau\) mode. After constraining the solutions with the consistent ranges of \(\sigma(pp \to bbA \to bb\tau\tau)\), a largest excess at about \(1.5 \sigma\) at 8 TeV center of mass (COM) energy and \(2\sigma\) at 13 TeV COM is observed for \(\tan\beta \sim 12\) and \(m_A \sim 28\) GeV in the \(\sigma(pp \to bbA \to bb\mu\mu)\) events.Electromagnetic Dalitz decays of decuplet to octet with the SU(3) flavor symmetry/breakinghttps://zbmath.org/1491.810312022-09-13T20:28:31.338867Z"Xu, Yuan-Guo"https://zbmath.org/authors/?q=ai:xu.yuanguo"Wang, Ru-Min"https://zbmath.org/authors/?q=ai:wang.rumin"Cheng, Xiao-Dong"https://zbmath.org/authors/?q=ai:cheng.xiaodong"Chang, Qin"https://zbmath.org/authors/?q=ai:chang.qinSummary: Motivated by the first measured \(\Delta^+ \to p e^+ e^-\) decay by the HADES Collaboration, electromagnetic Dalitz baryon decays from the spin \(\frac{3}{2}\) decuplet (\(T_{10}\)) to the spin \(\frac{1}{2}\) octet (\(T_8\)) baryons are investigated by using the SU(3) flavor symmetry/breaking in this paper. All decay amplitudes of \(T_{10} \to T_8 \ell^+ \ell^-\) (\(\ell = e, \mu\)) electromagnetic Dalitz decays could be related by the SU(3) flavor symmetry/breaking, so the amplitudes can be obtained by the measured branching ratio of \(\Delta^+ \to p e^+ e^-\) decay from the HADES Collaboration. The branching ratios, the lepton flavor universality, and the ratios \(\frac{\mathcal{B}(T_{10} \to T_8 \ell^+\ell^-)}{\mathcal{B}(T_{10} \to T_8 \gamma)}\) are predicted by the relevant experimental data. \(T_{10} \to T_8 \mu^+\mu^-\) electromagnetic Dalitz decays are studied for the first time. All predicted \(\mathcal{B}(T_{10} \to T_8 \ell^+ \ell^-)\) except \(\mathcal{B}(\Xi^{\ast 0} \to \Xi^0 \mu^+ \mu^-)\) and \(\mathcal{B}(\Xi^{\ast -} \to \Xi^- \mu^+ \mu^-)\) are on the order of \(\mathcal{O}(10^{-5}\text{--}10^{-7})\), and these decays could be observed and could be used to test the SU(3) flavor symmetry/breaking approach in the electromagnetic Dalitz decays by HADES, PANDA, BESIII, and other experiments in the near future.Generalized hydrodynamics in strongly interacting 1D Bose gaseshttps://zbmath.org/1491.810322022-09-13T20:28:31.338867Z"Malvania, Neel"https://zbmath.org/authors/?q=ai:malvania.neel"Zhang, Yicheng"https://zbmath.org/authors/?q=ai:zhang.yicheng"Le, Yuan"https://zbmath.org/authors/?q=ai:le.yuan"Dubail, Jerome"https://zbmath.org/authors/?q=ai:dubail.jerome"Rigol, Marcos"https://zbmath.org/authors/?q=ai:rigol.marcos"Weiss, David S."https://zbmath.org/authors/?q=ai:weiss.david-sSummary: The dynamics of strongly interacting many-body quantum systems are notoriously complex and difficult to simulate. A recently proposed theory called generalized hydrodynamics (GHD) promises to efficiently accomplish such simulations for nearly integrable systems. We test GHD with bundles of ultracold one-dimensional (1D) Bose gases by performing large trap quenches in both the strong and intermediate coupling regimes. We find that theory and experiment agree well over dozens of trap oscillations, for average dimensionless coupling strengths that range from 0.3 to 9.3. Our results show that GHD can accurately describe the quantum dynamics of a 1D nearly integrable experimental system even when particle numbers are low and density changes are large and fast.Entanglement transport and a nanophotonic interface for atoms in optical tweezershttps://zbmath.org/1491.810332022-09-13T20:28:31.338867Z"Đorđević, Tamara"https://zbmath.org/authors/?q=ai:dordevic.tamara"Samutpraphoot, Polnop"https://zbmath.org/authors/?q=ai:samutpraphoot.polnop"Ocola, Paloma L."https://zbmath.org/authors/?q=ai:ocola.paloma-l"Bernien, Hannes"https://zbmath.org/authors/?q=ai:bernien.hannes"Grinkemeyer, Brandon"https://zbmath.org/authors/?q=ai:grinkemeyer.brandon"Dimitrova, Ivana"https://zbmath.org/authors/?q=ai:dimitrova.ivana"Vuletić, Vladan"https://zbmath.org/authors/?q=ai:vuletic.vladan"Lukin, Mikhail D."https://zbmath.org/authors/?q=ai:lukin.mikhail-dSummary: The realization of an efficient quantum optical interface for multi-qubit systems is an outstanding challenge in science and engineering. Using two atoms in individually controlled optical tweezers coupled to a nanofabricated photonic crystal cavity, we demonstrate entanglement generation, fast nondestructive readout, and full quantum control of atomic qubits. The entangled state is verified in free space after being transported away from the cavity by encoding the qubits into long-lived states and using dynamical decoupling. Our approach bridges quantum operations at an optical link and in free space with a coherent one-way transport, potentially enabling an integrated optical interface for atomic quantum processors.Higher-dimensional supersymmetric microlaser arrayshttps://zbmath.org/1491.810342022-09-13T20:28:31.338867Z"Qiao, Xingdu"https://zbmath.org/authors/?q=ai:qiao.xingdu"Midya, Bikashkali"https://zbmath.org/authors/?q=ai:midya.bikashkali"Gao, Zihe"https://zbmath.org/authors/?q=ai:gao.zihe"Zhang, Zhifeng"https://zbmath.org/authors/?q=ai:zhang.zhifeng"Zhao, Haoqi"https://zbmath.org/authors/?q=ai:zhao.haoqi"Wu, Tianwei"https://zbmath.org/authors/?q=ai:wu.tianwei"Yim, Jieun"https://zbmath.org/authors/?q=ai:yim.jieun"Agarwal, Ritesh"https://zbmath.org/authors/?q=ai:agarwal.ritesh"Litchinitser, Natalia M."https://zbmath.org/authors/?q=ai:litchinitser.natalia-m"Feng, Liang"https://zbmath.org/authors/?q=ai:feng.liangSummary: The nonlinear scaling of complexity with the increased number of components in integrated photonics is a major obstacle impeding large-scale, phase-locked laser arrays. Here, we develop a higher-dimensional supersymmetry formalism for precise mode control and nonlinear power scaling. Our supersymmetric microlaser arrays feature phase-locked coherence and synchronization of all of the evanescently coupled microring lasers -- collectively oscillating in the fundamental transverse supermode -- which enables high-radiance, small-divergence, and single-frequency laser emission with a two-orders-of-magnitude enhancement in energy density. We also demonstrate the feasibility of structuring high-radiance vortex laser beams, which enhance the laser performance by taking full advantage of spatial degrees of freedom of light. Our approach provides a route for designing large-scale integrated photonic systems in both classical and quantum regimes.A novel Bethe ansatz scheme for the one-dimensional Hubbard modelhttps://zbmath.org/1491.820072022-09-13T20:28:31.338867Z"Yi, Yifei"https://zbmath.org/authors/?q=ai:yi.yifei"Qiao, Yi"https://zbmath.org/authors/?q=ai:qiao.yi"Cao, Junpeng"https://zbmath.org/authors/?q=ai:cao.junpeng"Yang, Wen-Li"https://zbmath.org/authors/?q=ai:yang.wenliSummary: We propose a novel characterization of the exact solution of the one-dimensional Hubbard model with unparallel boundary magnetic fields. The non-diagonal boundary terms break the \(U(1)\) symmetry of the system and the number of electrons with fixed spin is not conserved. Thus it is difficult to study the physical quantities in the thermodynamic limit based on the previously obtained inhomogeneous \(T\)-\(Q\) relation and Bethe ansatz equations. In order to solve this problem, we propose the \(t\)-\(W\) scheme. The basic idea is that the eigenvalues of the transfer matrix can be expressed by its zero-roots instead of the usual Bethe roots. This method allows us to study thermodynamic properties of the system such as the ground state, surface energy, charge and spin excitations. The \(t\)-\(W\) scheme is universal and can be applied to the systems either with or without \(U(1)\) symmetry.Thermoelectric effects in self-similar multibarrier structure based on monolayer graphenehttps://zbmath.org/1491.820252022-09-13T20:28:31.338867Z"Miniya, M."https://zbmath.org/authors/?q=ai:miniya.m"Oubram, O."https://zbmath.org/authors/?q=ai:oubram.o"Reynaud-Morales, A. G."https://zbmath.org/authors/?q=ai:reynaud-morales.a-g"Rodríguez-Vargas, I."https://zbmath.org/authors/?q=ai:rodriguez-vargas.i"Gaggero-Sager, L. M."https://zbmath.org/authors/?q=ai:gaggero-sager.l-mInfrared scaling for a graviton condensatehttps://zbmath.org/1491.830042022-09-13T20:28:31.338867Z"Bose, Sougato"https://zbmath.org/authors/?q=ai:bose.sougato"Mazumdar, Anupam"https://zbmath.org/authors/?q=ai:mazumdar.anupam"Toroš, Marko"https://zbmath.org/authors/?q=ai:toros.markoSummary: The coupling between gravity and matter provides an intriguing length scale in the infrared for theories of gravity within Einstein-Hilbert action and beyond. In particular, we will show that such an infrared length scale is determined by the number of gravitons \(N_g \gg 1\) associated to a given mass in the non-relativistic limit. After tracing out the matter degrees of freedom, the graviton vacuum is found to be in a displaced vacuum with an occupation number of gravitons \(N_g \gg 1\). In the infrared, the length scale appears to be \(L = \sqrt{N_g}\ell_p\), where \(L\) is the new infrared length scale, and \(\ell_p\) is the Planck length. In a specific example, we have found that the infrared length scale is greater than the Schwarzschild radius for a slowly moving in-falling thin shell of matter. We will argue that the appearance of such an infrared length scale in higher curvature theories of gravity, such as in quadratic and cubic curvature theories of gravity, is also expected. Furthermore, we will show that gravity is fundamentally different from the electromagnetic interaction where the number of photons, \(N_p\), is the \textit{fine structure constant} after tracing out an electron wave function.On the expected backreaction during preheatinghttps://zbmath.org/1491.830062022-09-13T20:28:31.338867Z"Armendariz-Picon, C."https://zbmath.org/authors/?q=ai:armendariz-picon.cristian(no abstract)Gravity in the infrared and effective nonlocal modelshttps://zbmath.org/1491.830072022-09-13T20:28:31.338867Z"Belgacem, Enis"https://zbmath.org/authors/?q=ai:belgacem.enis"Dirian, Yves"https://zbmath.org/authors/?q=ai:dirian.yves"Finke, Andreas"https://zbmath.org/authors/?q=ai:finke.andreas"Foffa, Stefano"https://zbmath.org/authors/?q=ai:foffa.stefano"Maggiore, Michele"https://zbmath.org/authors/?q=ai:maggiore.michele(no abstract)Unveiling the Galileon in a three-body system: scalar and gravitational wave productionhttps://zbmath.org/1491.830082022-09-13T20:28:31.338867Z"Brax, Philippe"https://zbmath.org/authors/?q=ai:brax.philippe"Heisenberg, Lavinia"https://zbmath.org/authors/?q=ai:heisenberg.lavinia"Kuntz, Adrien"https://zbmath.org/authors/?q=ai:kuntz.adrien(no abstract)Probing multi-step electroweak phase transition with multi-peaked primordial gravitational waves spectrahttps://zbmath.org/1491.830132022-09-13T20:28:31.338867Z"Morais, António P."https://zbmath.org/authors/?q=ai:morais.antonio-p"Pasechnik, Roman"https://zbmath.org/authors/?q=ai:pasechnik.roman(no abstract)Cosmological collider signatures of massive vectors from non-Gaussian gravitational waveshttps://zbmath.org/1491.830152022-09-13T20:28:31.338867Z"Wang, Yi"https://zbmath.org/authors/?q=ai:wang.yi.10|wang.yi.4|wang.yi.7|wang.yi.6|wang.yi.9|wang.yi.3|wang.yi.5|wang.yi.8|wang.yi.1|wang.yi.2"Zhu, Yuhang"https://zbmath.org/authors/?q=ai:zhu.yuhang(no abstract)Casimir effect in a weak gravitational field: Schwinger's approachhttps://zbmath.org/1491.830162022-09-13T20:28:31.338867Z"Sorge, Francesco"https://zbmath.org/authors/?q=ai:sorge.francescoGRAMSES: a new route to general relativistic \(N\)-body simulations in cosmology. II: Initial conditionshttps://zbmath.org/1491.830172022-09-13T20:28:31.338867Z"Barrera-Hinojosa, Cristian"https://zbmath.org/authors/?q=ai:barrera-hinojosa.cristian"Li, Baojiu"https://zbmath.org/authors/?q=ai:li.baojiuGeometric dark matterhttps://zbmath.org/1491.830192022-09-13T20:28:31.338867Z"Demir, Durmuş"https://zbmath.org/authors/?q=ai:demir.durmus-ali"Puliçe, Beyhan"https://zbmath.org/authors/?q=ai:pulice.beyhan(no abstract)Symmetric scalarshttps://zbmath.org/1491.830212022-09-13T20:28:31.338867Z"Grall, Tanguy"https://zbmath.org/authors/?q=ai:grall.tanguy"Jazayeri, Sadra"https://zbmath.org/authors/?q=ai:jazayeri.sadra"Pajer, Enrico"https://zbmath.org/authors/?q=ai:pajer.enrico(no abstract)Stochastic axion dark matter in axion landscapehttps://zbmath.org/1491.830242022-09-13T20:28:31.338867Z"Nakagawa, Shota"https://zbmath.org/authors/?q=ai:nakagawa.shota"Takahashi, Fuminobu"https://zbmath.org/authors/?q=ai:takahashi.fuminobu"Yin, Wen"https://zbmath.org/authors/?q=ai:yin.wen(no abstract)The evolution of the FRW universe with decaying metastable dark energy -- a dynamical system analysishttps://zbmath.org/1491.830262022-09-13T20:28:31.338867Z"Szydłowski, Marek"https://zbmath.org/authors/?q=ai:szydlowski.marek"Stachowski, Aleksander"https://zbmath.org/authors/?q=ai:stachowski.aleksander"Urbanowski, Krzysztof"https://zbmath.org/authors/?q=ai:urbanowski.krzysztof(no abstract)Consistent Blandford-Znajek expansionhttps://zbmath.org/1491.830272022-09-13T20:28:31.338867Z"Armas, Jay"https://zbmath.org/authors/?q=ai:armas.jay"Cai, Yangyang"https://zbmath.org/authors/?q=ai:cai.yangyang"Compère, Geoffrey"https://zbmath.org/authors/?q=ai:compere.geoffrey"Garfinkle, David"https://zbmath.org/authors/?q=ai:garfinkle.david"Gralla, Samuel E."https://zbmath.org/authors/?q=ai:gralla.samuel-e(no abstract)Comparing parametric and non-parametric velocity-dependent one-scale models for domain wall evolutionhttps://zbmath.org/1491.830292022-09-13T20:28:31.338867Z"Avelino, P. P."https://zbmath.org/authors/?q=ai:avelino.pedro-pina(no abstract)Spiky CMB distortions from primordial bubbleshttps://zbmath.org/1491.830322022-09-13T20:28:31.338867Z"Deng, Heling"https://zbmath.org/authors/?q=ai:deng.heling(no abstract)Spontaneous radiation of black holeshttps://zbmath.org/1491.830362022-09-13T20:28:31.338867Z"Zeng, Ding-fang"https://zbmath.org/authors/?q=ai:zeng.ding-fangSummary: We provide an explicitly hermitian hamiltonian description for the spontaneous radiation of black holes, which is a many-level, multiple-degeneracy generalization of the usual Janeys-Cummings model for two-level atoms. We show that under single-particle radiation and standard Wigner-Wiesskopf approximation, our model yields exactly thermal type power spectrum as hawking radiation requires. While in the many-particle radiation cases, numeric methods allow us to follow the evolution of microscopic state of a black hole exactly, from which we can get the firstly increasing then decreasing entropy variation trend for the radiation particles just as the Page-curve exhibited. Basing on this model analysis, we claim that two ingredients are necessary for resolutions of the information missing puzzle, a spontaneous radiation like mechanism for the production of hawking particles and proper account of the macroscopic superposition happening in the full quantum description of a black hole radiation evolution and, the working logic of replica wormholes is an effect account of this latter ingredient.
As the basis for our interpretation of black hole Hawking radiation as their spontaneous radiation, we also provide a fully atomic like inner structure models for their microscopic states definition and origins of their Bekenstein-Hawking entropy, that is, exact solution families to the Einstein equation sourced by matter constituents oscillating across the central point and their quantization. Such a first quantization model for black holes' microscopic state is non necessary for our spontaneous radiation description, but has advantages comparing with other alternatives, such as string theory fuzzball or brick wall models.Generalized uncertainty principle effects in the Hořava-Lifshitz quantum theory of gravityhttps://zbmath.org/1491.830372022-09-13T20:28:31.338867Z"García-Compeán, H."https://zbmath.org/authors/?q=ai:garcia-compean.hugo|garcia-compean.hector"Mata-Pacheco, D."https://zbmath.org/authors/?q=ai:mata-pacheco.dSummary: The Wheeler-DeWitt equation for a Kantowski-Sachs metric in Hořava-Lifshitz gravity with a set of coordinates in minisuperspace that obey a generalized uncertainty principle is studied. We first study the equation coming from a set of coordinates that obey the usual uncertainty principle and find analytic solutions in the infrared as well as a particular ultraviolet limit that allows us to find the solution found in Hořava-Lifshitz gravity with projectability and with detailed balance but now as an approximation of the theory without detailed balance. We then consider the coordinates that obey the generalized uncertainty principle by modifying the previous equation using the relations between both sets of coordinates. We describe two possible ways of obtaining the Wheeler-DeWitt equation. One of them is useful to present the general equation but it is found to be very difficult to solve. Then we use the other proposal to study the limiting cases considered before, that is, the infrared limit that can be compared to the equation obtained by using general relativity and the particular ultraviolet limit. For the second limit we use a ultraviolet approximation and then solve analytically the resulting equation. We find that and oscillatory behaviour is possible in this context but it is not a general feature for any values of the parameters involved.Covariant quantum corrections to a scalar field model inspired by nonminimal natural inflationhttps://zbmath.org/1491.830402022-09-13T20:28:31.338867Z"Aashish, Sandeep"https://zbmath.org/authors/?q=ai:aashish.sandeep"Panda, Sukanta"https://zbmath.org/authors/?q=ai:panda.sukanta(no abstract)Constant-roll in the Palatini-\(R^2\) modelshttps://zbmath.org/1491.830412022-09-13T20:28:31.338867Z"Antoniadis, Ignatios"https://zbmath.org/authors/?q=ai:antoniadis.ignatios"Lykkas, Angelos"https://zbmath.org/authors/?q=ai:lykkas.angelos"Tamvakis, Kyriakos"https://zbmath.org/authors/?q=ai:tamvakis.kyriakos(no abstract)Banks-Zaks cosmology, inflation, and the big bang singularityhttps://zbmath.org/1491.830432022-09-13T20:28:31.338867Z"Artymowski, Michal"https://zbmath.org/authors/?q=ai:artymowski.michal"Ben-Dayan, Ido"https://zbmath.org/authors/?q=ai:ben-dayan.ido"Kumar, Utkarsh"https://zbmath.org/authors/?q=ai:kumar.utkarsh(no abstract)Detuning primordial black hole dark matter with early matter domination and axion monodromyhttps://zbmath.org/1491.830472022-09-13T20:28:31.338867Z"Ballesteros, Guillermo"https://zbmath.org/authors/?q=ai:ballesteros.guillermo"Rey, Julián"https://zbmath.org/authors/?q=ai:rey.julian"Rompineve, Fabrizio"https://zbmath.org/authors/?q=ai:rompineve.fabrizio(no abstract)Superconformal generalizations of auxiliary vector modified polynomial \(f(R)\) theorieshttps://zbmath.org/1491.830492022-09-13T20:28:31.338867Z"Boran, Sibel"https://zbmath.org/authors/?q=ai:boran.sibel"Kahya, Emre Onur"https://zbmath.org/authors/?q=ai:kahya.emre-onur"Ozdemir, Nese"https://zbmath.org/authors/?q=ai:ozdemir.nese"Ozkan, Mehmet"https://zbmath.org/authors/?q=ai:ozkan.mehmet"Zorba, Utku"https://zbmath.org/authors/?q=ai:zorba.utku(no abstract)Pseudosmooth tribrid inflation in SU(5)https://zbmath.org/1491.830522022-09-13T20:28:31.338867Z"Masoud, Muhammad Atif"https://zbmath.org/authors/?q=ai:masoud.muhammad-atif"Rehman, Mansoor Ur"https://zbmath.org/authors/?q=ai:rehman.mansoor-ur"Shafi, Qaisar"https://zbmath.org/authors/?q=ai:shafi.qaisar(no abstract)Destabilization of the EW vacuum in non-minimally coupled inflationhttps://zbmath.org/1491.830542022-09-13T20:28:31.338867Z"Rusak, Stanislav"https://zbmath.org/authors/?q=ai:rusak.stanislav(no abstract)Initial conditions for plateau inflation: a case studyhttps://zbmath.org/1491.830552022-09-13T20:28:31.338867Z"Tenkanen, Tommi"https://zbmath.org/authors/?q=ai:tenkanen.tommi"Tomberg, Eemeli"https://zbmath.org/authors/?q=ai:tomberg.eemeli-s(no abstract)Inflation without gauge redundancyhttps://zbmath.org/1491.830562022-09-13T20:28:31.338867Z"Urbano, Alfredo"https://zbmath.org/authors/?q=ai:urbano.alfredo(no abstract)More on the open string pair productionhttps://zbmath.org/1491.830572022-09-13T20:28:31.338867Z"Lu, J. X."https://zbmath.org/authors/?q=ai:lu.jiaxin|lu.jiaxi.1|lu.junxu|lu.junxiao|lu.jingxiang|lu.junxiang|lu.jianxin|lu.jinxiang|lu.jiaxuan"Zhang, Nan"https://zbmath.org/authors/?q=ai:zhang.nan.1Summary: Motivated by the recent work [the first author, J. High Energy Phys. 2019, No. 10, Paper No. 238, 13 p. (2019; Zbl 1427.83109)] by one of the present authors, we here report that there exist two new systems, namely, D3/(F, D1) and D3/(D3, (F, D1)), either of which can give rise to a much larger sizable open string pair production rate at a condition much relaxed. Here the D3 is taken as our own (1 + 3)-dimensional world while the non-threshold bound state (F, D1) or (D3, (F, D1)) is placed parallel nearby in the directions transverse to both our D3 world and the non-threshold bound state considered.Cosmic microwave background anisotropy numerical solution (CMBAns). I: An introduction to \(C_l\) calculationhttps://zbmath.org/1491.830592022-09-13T20:28:31.338867Z"Das, Santanu"https://zbmath.org/authors/?q=ai:das.santanu-kumar"Phan, Anh"https://zbmath.org/authors/?q=ai:phan.anh-dung|phan.anh-vu|phan.anh-huy(no abstract)The EFT likelihood for large-scale structurehttps://zbmath.org/1491.850032022-09-13T20:28:31.338867Z"Cabass, Giovanni"https://zbmath.org/authors/?q=ai:cabass.giovanni"Schmidt, Fabian"https://zbmath.org/authors/?q=ai:schmidt.fabian(no abstract)Multipoles of the relativistic galaxy bispectrumhttps://zbmath.org/1491.850042022-09-13T20:28:31.338867Z"de Weerd, Eline M."https://zbmath.org/authors/?q=ai:de-weerd.eline-m"Clarkson, Chris"https://zbmath.org/authors/?q=ai:clarkson.chris-a"Jolicoeur, Sheean"https://zbmath.org/authors/?q=ai:jolicoeur.sheean"Maartens, Roy"https://zbmath.org/authors/?q=ai:maartens.roy"Umeh, Obinna"https://zbmath.org/authors/?q=ai:umeh.obinna(no abstract)Optimal and two-step adaptive quantum detector tomographyhttps://zbmath.org/1491.930292022-09-13T20:28:31.338867Z"Xiao, Shuixin"https://zbmath.org/authors/?q=ai:xiao.shuixin"Wang, Yuanlong"https://zbmath.org/authors/?q=ai:wang.yuanlong"Dong, Daoyi"https://zbmath.org/authors/?q=ai:dong.daoyi"Zhang, Jun"https://zbmath.org/authors/?q=ai:zhang.jun.7|zhang.jun.5|zhang.jun|zhang.jun.3|zhang.jun.10|zhang.jun.1|zhang.jun.4|zhang.jun.8|zhang.jun.2|zhang.jun.9|zhang.jun.6Summary: Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we design optimal probe states for detector estimation based on the minimum upper bound of the mean squared error (UMSE) and the maximum robustness. We establish the minimum UMSE and the minimum condition number for quantum detectors and provide concrete examples that can achieve optimal detector tomography. In order to enhance the estimation precision, we also propose a two-step adaptive detector tomography algorithm to optimize the probe states adaptively based on a modified fidelity index. We present a sufficient condition on when the estimation error of our two-step strategy scales inversely proportional to the number of state copies. Moreover, the superposition of coherent states is used as probe states for quantum detector tomography and the estimation error is analyzed. Numerical results demonstrate the effectiveness of both the proposed optimal and adaptive quantum detector tomography methods.Quantum image processinghttps://zbmath.org/1491.940012022-09-13T20:28:31.338867Z"Yan, Fei"https://zbmath.org/authors/?q=ai:yan.fei"Venegas-Andraca, Salvador E."https://zbmath.org/authors/?q=ai:venegas-andraca.salvador-eliasPublisher's description: This book provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends. It offers a valuable reference resource for graduate students and researchers interested in this emerging interdisciplinary field.Practical post-quantum few-time verifiable random function with applications to Algorandhttps://zbmath.org/1491.940472022-09-13T20:28:31.338867Z"Esgin, Muhammed F."https://zbmath.org/authors/?q=ai:esgin.muhammed-f"Kuchta, Veronika"https://zbmath.org/authors/?q=ai:kuchta.veronika"Sakzad, Amin"https://zbmath.org/authors/?q=ai:sakzad.amin"Steinfeld, Ron"https://zbmath.org/authors/?q=ai:steinfeld.ron"Zhang, Zhenfei"https://zbmath.org/authors/?q=ai:zhang.zhenfei"Sun, Shifeng"https://zbmath.org/authors/?q=ai:sun.shifeng"Chu, Shumo"https://zbmath.org/authors/?q=ai:chu.shumoSummary: In this work, we introduce the first practical post-quantum verifiable random function (VRF) that relies on well-known (module) lattice problems, namely Module-SIS and Module-LWE. Our construction, named LB-VRF, results in a VRF value of only 84 bytes and a proof of around only 5 KB (in comparison to several MBs in earlier works), and runs in about 3 ms for evaluation and about 1 ms for verification.
In order to design a practical scheme, we need to restrict the number of VRF outputs per key pair, which makes our construction few-time. Despite this restriction, we show how our few-time LB-VRF can be used in practice and, in particular, we estimate the performance of Algorand using LB-VRF. We find that, due to the significant increase in the communication size in comparison to classical constructions, which is inherent in all existing lattice-based schemes, the throughput in LB-VRF-based consensus protocol is reduced, but remains practical. In particular, in a medium-sized network with 100 nodes, our platform records a \(1.14 \times\) to \(3.4 \times\) reduction in throughput, depending on the accompanying signature used. In the case of a large network with 500 nodes, we can still maintain at least 24 transactions per second. This is still much better than Bitcoin, which processes only about 5 transactions per second.
For the entire collection see [Zbl 1489.94004].Full key recovery side-channel attack against ephemeral SIKE on the cortex-M4https://zbmath.org/1491.940502022-09-13T20:28:31.338867Z"Genêt, Aymeric"https://zbmath.org/authors/?q=ai:genet.aymeric"de Guertechin, Natacha Linard"https://zbmath.org/authors/?q=ai:de-guertechin.natacha-linard"Kaluđerović, Novak"https://zbmath.org/authors/?q=ai:kaluderovic.novakSummary: This paper describes the first practical single-trace side-channel power analysis of SIKE. While SIKE is a post-quantum key exchange, the scheme still relies on a secret elliptic curve scalar multiplication which involves a loop of a double-and-add procedure, of which each iteration depends on a single bit of the private key. The attack therefore exploits the nature of elliptic curve point addition formulas which require the same function to be executed multiple times. We show how a single trace of a loop iteration can be segmented into several power traces on which 32-bit words can be hypothesised based on the value of a single private key bit. This segmentation enables a classical correlation power analysis in an extend-and-prune approach. Further error-correction techniques based on depth-search are suggested. The attack is explicitly geared towards and experimentally verified on an STM32F3 featuring a Cortex-M4 microcontroller which runs the SIKEp434 implementation adapted to 32-bit ARM that is part of the official implementations of SIKE. We obtained a resounding 100\% success rate recovering the full private key in each experiment. We argue that our attack defeats many countermeasures which were suggested in a previous power analysis of SIKE, and finally show that the well-known countermeasure of projective coordinate randomisation stops the attack with a negligible overhead.
For the entire collection see [Zbl 1489.94002].Misdirection steganographyhttps://zbmath.org/1491.940592022-09-13T20:28:31.338867Z"Mihara, Takashi"https://zbmath.org/authors/?q=ai:mihara.takashiSummary: Information is one of the most important resources in this world. Therefore, we must protect it from third parties. A typical method for protecting information contents is cryptography. We use cryptography to prevent secret information from leaking to third parties. However, we will use steganography to conceal the existence of information because cryptography cannot achieve this function. Many steganographic techniques have been also proposed as well as cryptography. In this paper, we propose a different type of steganography called misdirection steganography. Our steganography transfers two kinds of secret data, true secret data and decoy secret data, as data embedding into cover data, and the process embedding the true secret data depends on how to embed the decoy secret data, i.e., the information about embedding the decoy secret data is also required to extract the true secret data. Our aim is to transfer true secret data in secret by letting third parties pay attention to decoy secret data. In other words, misdirection in the proposed steganography techniques is caused by the fact that the decoy secret data protect the true secret data against third parties.Resistance of isogeny-based cryptographic implementations to a fault attackhttps://zbmath.org/1491.940672022-09-13T20:28:31.338867Z"Tasso, Élise"https://zbmath.org/authors/?q=ai:tasso.elise"De Feo, Luca"https://zbmath.org/authors/?q=ai:de-feo.luca"El Mrabet, Nadia"https://zbmath.org/authors/?q=ai:el-mrabet.nadia"Pontié, Simon"https://zbmath.org/authors/?q=ai:pontie.simonSummary: The threat of quantum computers has sparked the development of a new kind of cryptography to resist their attacks. Isogenies between elliptic curves are one of the tools used for such cryptosystems. They are championed by SIKE (Supersingular isogeny key encapsulation), an ``alternate candidate'' of the third round of the NIST Post-Quantum Cryptography Standardization Process. While all candidates are believed to be mathematically secure, their implementations may be vulnerable to hardware attacks. In this work we investigate for the first time whether Ti's theoretical fault injection attack [\textit{Y. B. Ti}, Lect. Notes Comput. Sci. 10346, 107--122 (2017; Zbl 1437.94075)] is exploitable in practice. We also examine suitable countermeasures. We manage to recover the secret thanks to electromagnetic fault injection on an ARM Cortex A53 using a correct and an altered public key generation. Moreover we propose a suitable countermeasure to detect faults that has a low overhead as it takes advantage of a redundancy already present in SIKE implementations.
For the entire collection see [Zbl 1489.94002].Access control encryption from group encryptionhttps://zbmath.org/1491.940712022-09-13T20:28:31.338867Z"Wang, Xiuhua"https://zbmath.org/authors/?q=ai:wang.xiuhua"Wong, Harry W. H."https://zbmath.org/authors/?q=ai:wong.harry-w-h"Chow, Sherman S. M."https://zbmath.org/authors/?q=ai:chow.sherman-s-mSummary: Access control encryption (ACE) enforces both read and write permissions. It kills off any unpermitted subliminal message channel via the help of a sanitizer who knows neither of the plaintext, its sender and receivers, nor the access control policy. This work aims to solve the open problem left by the seminal work of \textit{I. Damgård} et al. [Lect. Notes Comput. Sci. 9986, 547--576 (2016; Zbl 1400.94138)], namely, ``to construct practically interesting ACE from noisy, post-quantum assumptions such as LWE.'' We start with revisiting group encryption (GE), which allows anyone to encrypt to a certified group member, whom remains anonymous unless the opening authority decided to reveal him/her. We propose: 1) the notion of sanitizable GE (SGE), with specific changes for non-interactive proof, 2) the notion of traceable ACE (tACE), which helps damage control by tracing after-the-fact if some secret were leaked unluckily, 3) a generic construction of (t)ACE for equality policy (ACE-EP) from SGE, 4) a generic construction of ACE for general policy from ACE-EP, 5) a lattice-based instantiation of SGE, which comes with 6) a simple mechanism for checking that the randomness of ciphertexts can span the randomness space.
For the entire collection see [Zbl 1482.94010].