Recent zbMATH articles in MSC 82https://zbmath.org/atom/cc/822022-11-17T18:59:28.764376ZWerkzeugMinimum-perimeter lattice animals and the constant-isomer conjecturehttps://zbmath.org/1496.050242022-11-17T18:59:28.764376Z"Barequet, Gill"https://zbmath.org/authors/?q=ai:barequet.gill"Ben-Shachar, Gil"https://zbmath.org/authors/?q=ai:ben-shachar.gilSummary: We consider minimum-perimeter lattice animals, providing a set of conditions which are sufficient for a lattice to have the property that inflating all minimum-perimeter animals of a certain size yields (without repetitions) all minimum-perimeter animals of a new, larger size. We demonstrate this result on the two-dimensional square and hexagonal lattices. In addition, we characterize the sizes of minimum-perimeter animals on these lattices that are not created by inflating members of another set of minimum-perimeter animals.Martin boundary of killed random walks on isoradial graphshttps://zbmath.org/1496.310062022-11-17T18:59:28.764376Z"Boutillier, Cédric"https://zbmath.org/authors/?q=ai:boutillier.cedric"Raschel, Kilian"https://zbmath.org/authors/?q=ai:raschel.kilianThis article discusses killed planar random walks on isoradial graphs. Unlike the lattice case, isoradial graphs present some difficulties such as: not translation invariant, do not admit any group structure and are spatially non-homogeneous. In the current work, the authors compute the asymptotics of the Martin kernel, deduce the Martin boundary and show its minimality.
Reviewer: Marius Ghergu (Dublin)Limit theorems for Jacobi ensembles with large parametershttps://zbmath.org/1496.330102022-11-17T18:59:28.764376Z"Hermann, Kilian"https://zbmath.org/authors/?q=ai:hermann.kilian"Voit, Michael"https://zbmath.org/authors/?q=ai:voit.michaelSummary: Consider \(\beta\)-Jacobi ensembles on the alcoves
\[
A:=\{ x\in\mathbb{R}^N \mid -1\leq x_1\leq \cdots\leq x_N\leq 1\}
\]
with parameters \(k_1,k_2,k_3\geq 0\). In the freezing case \((k_1,k_2,k_3)=\kappa\cdot (a,b,1)\) with \(a,b>0\) fixed and \(\kappa\to\infty\), we derive a central limit theorem. The drift and covariance matrix of the limit are expressed via the zeros of classical Jacobi polynomials. We also determine the eigenvalues and eigenvectors of the covariance matrices. Our results are related to corresponding limits for \(\beta\)-Hermite and Laguerre ensembles for \(\beta\to\infty\).On the multiscale Landau-Lifshitz-Gilbert equation: two-scale convergence and stability analysishttps://zbmath.org/1496.350372022-11-17T18:59:28.764376Z"Chen, Jingrun"https://zbmath.org/authors/?q=ai:chen.jingrun.1"Du, Rui"https://zbmath.org/authors/?q=ai:du.rui"Ma, Zetao"https://zbmath.org/authors/?q=ai:ma.zetao"Sun, Zhiwei"https://zbmath.org/authors/?q=ai:sun.zhiwei|sun.zhi-wei|sun.zhi-wei.1"Zhang, Lei"https://zbmath.org/authors/?q=ai:zhang.lei.5Homogenization results for a Landau-Lifshitz-Gilbert equation in composite materials with transmission defectshttps://zbmath.org/1496.350382022-11-17T18:59:28.764376Z"Choquet, C."https://zbmath.org/authors/?q=ai:choquet.catherine"Ouhadan, M."https://zbmath.org/authors/?q=ai:ouhadan.mohamed"Tilioua, M."https://zbmath.org/authors/?q=ai:tilioua.mouhcineSummary: We study the homogenization of Landau-Lifshitz-Gilbert equation in a \(\epsilon\)-periodic composite material formed by two constituents, separated by an imperfect interface \(\Gamma^\epsilon\), on which we prescribe the continuity of the conormal derivatives and a jump of the solution proportional to the conormal derivative, by means of a coefficient of order \(\epsilon^\gamma\). We use the periodic unfolding method together with extension operators for handling the nonlinearities to identify the limit problem when tuning up the parameter \(\gamma\) in \(\mathbb{R}\).Sufficient conditions for the continuity of inertial manifolds for singularly perturbed problemshttps://zbmath.org/1496.350972022-11-17T18:59:28.764376Z"Bonfoh, Ahmed"https://zbmath.org/authors/?q=ai:bonfoh.ahmed-sSummary: We consider a nonlinear evolution equation in the form
\[
\mathrm{U_t + A_\varepsilon U + N_\varepsilon G_\varepsilon (U)} = 0,
\tag{\(\mathrm{E}_{\varepsilon}\)}
\]
together with its singular limit problem as \(\varepsilon\to 0\)
\[
U_t+ A U+ \mathrm{N} G(U) = 0,
\tag{E}
\]
where \(\varepsilon\in (0,1]\) (possibly \(\varepsilon = 0\)), \(\mathrm{A}_\varepsilon\) and \(\mathrm{A}\) are linear closed (possibly) unbounded operators, \(\mathrm{N}_\varepsilon\) and \(\mathrm{N}\) are linear (possibly) unbounded operators, \(\mathrm{G}_\varepsilon\) and \(\mathrm{G}\) are nonlinear functions. We give sufficient conditions on \(\mathrm{A}_\varepsilon\), \(\mathrm{N}_\varepsilon\) and \(\mathrm{G}_\varepsilon\) (and also \(\mathrm{A}, \mathrm{N}\) and \(\mathrm{G})\) that guarantee not only the existence of an inertial manifold of dimension independent of \(\varepsilon\) for \((E_\varepsilon)\) on a Banach space \(\mathcal{H}\), but also the Hölder continuity, lower and upper semicontinuity at \(\varepsilon = 0\) of the intersection of the inertial manifold with a bounded absorbing set. Applications to higher order viscous Cahn-Hilliard-Oono equations, the hyperbolic type equations and the phase-field systems, subject to either Neumann or Dirichlet boundary conditions (BC) (in which case \(\Omega\subset \mathbb{R}^d\) is a bounded domain with smooth boundary) or periodic BC (in which case \(\Omega = \Pi_{i = 1}^d (0,L_i), \, L_i>0)\), \(d = 1\), 2 or 3, are considered. These three classes of dissipative equations read
\[
\phi_t+N(\varepsilon \phi_t+N^{\alpha+1} \phi +N\phi + g(\phi))+\sigma\phi = 0,\quad\alpha\in\mathbb{N},\\
\tag{\(\mathrm{P}_\varepsilon\)}
\]
\[
\varepsilon \phi_{tt}+\phi_t+N^\alpha(N \phi + g(\phi))+ \sigma\phi = 0,\quad\alpha = 0, 1,\\
\tag{\(\mathrm{H}_\varepsilon\)}
\]
and
\[
\begin{cases}
\phi_t+N^\alpha (N \phi + g(\phi)-u)+\sigma\phi = 0,\\
\varepsilon u_t+\phi_t+N u = 0,
\end{cases}
\alpha = 0, 1
\tag{\(\mathrm{S}_\varepsilon\)}
\]
respectively, where \(\sigma\ge 0\) and the Laplace operator is defined as
\[
N = -\Delta:\mathscr{D}(N) = \{\psi\in H^2(\Omega),\,\psi \text{ subject to the BC}\}\to \dot L^2(\Omega) \text{ or }L^2(\Omega).
\]
We assume that, for a given real number \(\mathfrak{c}_1>0,\) there exists a positive integer \(n = n(\mathfrak{c}_1)\) such that \(\lambda_{n+1}-\lambda_n>\mathfrak{c}_1\), where \(\{\lambda_k\}_{k\in\mathbb{N}^*}\) are the eigenvalues of \(N\). There exists a real number \(\mathscr{M}>0\) such that the nonlinear function \(g: V_j\to V_j\) satisfies the conditions \(\|g(\psi)\|_j\le\mathscr{M}\) and \(\|g(\psi)-g(\varphi)\|_{V_j}\le\mathscr{M}\|\psi-\varphi\|_{V_j}\), \(\forall\psi\), \(\varphi\in V_j\), where \(V_j = \mathscr{D}(N^{j/2})\), \(j = 1\) for Problems \((P_\epsilon)\) and \((S_\epsilon)\) and \(j = 0\), \(2\alpha\) for Problem \((H_\epsilon)\). We further require \(g\in{\mathcal C}^1(V_j, V_j)\), \(\|g'(\psi)\varphi\|_j\le\mathscr{M}\|\varphi\|_j\) for Problems \((H_\epsilon)\) and \((S_\epsilon)\).Fast localization of eigenfunctions via smoothed potentialshttps://zbmath.org/1496.351792022-11-17T18:59:28.764376Z"Lu, Jianfeng"https://zbmath.org/authors/?q=ai:lu.jianfeng"Murphey, Cody"https://zbmath.org/authors/?q=ai:murphey.cody"Steinerberger, Stefan"https://zbmath.org/authors/?q=ai:steinerberger.stefanThe authors are interested in the problem of predicting localized eigenfunctions \(\phi\) of Schrödinger operators of the form \(-\Delta + V\) on bounded domains in \(\mathbb{R}^d\), where the potential \(V\) is assumed to be rapidly varying.
They build on a recent work of the third author [Commun. Partial Differ. Equations 46, No. 7, 1262--1279 (2021; Zbl 1487.35200)] who introduced an alternative to the landscape function approach of \textit{M. Filoche} and \textit{S. Mayboroda} [``Universal mechanism for Anderson and weak localization'', Proc. Natl. Acad. Sci. USA, 109, No. 37, 14761--14766 (2012; \url{doi:10.1073/pnas.1120432109})], who use the minima of the function \(1/u\), where \(u\) solves \((-\Delta + V)u=1\) (plus boundary conditions), to predict the location of localized eigenfunctions very well.
The alternative approach introduced by the third author comes from observing that the eigenvalue equation can be rewritten in a slightly smoothed form, \[ -\Delta \phi(x) + (V \ast k_t)(x)\phi(x) = \lambda\phi(x) + \text{error} (x,t) \] for a specially chosen kernel \(k_t\), a ``universal convolution kernel'' \[ k_t(x) = \frac{1}{t} \int_0^t \frac{\text{exp}(-\|x\|^2/4s)}{(4\pi s)^{d/2}}\,ds, \] such that the error can be controlled in terms of \(\phi\) and \(\|V\|_\infty\) only (for each fixed \(x\) and for the correct power of \(t\)). An analysis shows that the function \(k_t \ast V\) should then (for suitable values of \(t\)) act as a rapidly computable landscape function, with very similar behaviour to the one of Filoche and Mayboroda.
In the paper under review, the authors give an alternative representation of \(k_t\) well-suited to numerical computations, as it reduces the problem of calculating \(k_t \ast V\) to two applications of the Fast Fourier Transform. They present the corresponding algorithm, and also sketch how it can be extended to similar operators such as fractional Laplacians \(-\Delta^\alpha + V\) and Bilaplacians \((-\Delta)^2+V\).
They also conduct a numerical analysis in a prototypical setting, showing among other things that their landscape function does in fact approximate the one of Filoche and Mayboroda [loc. cit.] quite well.
Reviewer: James Bernard Kennedy (Lisboa)On dissipative solutions to a simplified hyperbolic Ericksen-Leslie system of liquid crystalshttps://zbmath.org/1496.353092022-11-17T18:59:28.764376Z"Cheng, Feng"https://zbmath.org/authors/?q=ai:cheng.feng"Jiang, Ning"https://zbmath.org/authors/?q=ai:jiang.ning"Luo, Yi-Long"https://zbmath.org/authors/?q=ai:luo.yi-longSummary: We study dissipative solutions to a 3D simplified hyperbolic Ericksen-Leslie system for liquid crystals with Ginzburg-Landau approximation. First, we establish a weak-strong stability principle, which leads to a suitable notion of dissipative solutions to the hyperbolic Ericksen-Leslie system. Then, we introduce a regularized system to approximate the original system, for which we can prove the existence of global-in-time weak solutions. Finally, we prove that there is at least one dissipative solution for this simplified hyperbolic Ericksen-Leslie system.The mean-field approximation for higher-dimensional Coulomb flows in the scaling-critical \(L^\infty\) spacehttps://zbmath.org/1496.353242022-11-17T18:59:28.764376Z"Rosenzweig, Matthew"https://zbmath.org/authors/?q=ai:rosenzweig.matthewThe author considers the relationship between first-order systems of particles with binary interactions governed by the Coulomb potential and a certain nonlinear first-order scalar partial differential equation which evokes vortex density models for superconductivity and superfluidity. The empirical measure of such a Coulomb system is proved to be a weak solution of this nonlinear scalar partial differential equation. Let \(d\) be the dimension of the space where the motion of particles takes place. In the case when \(d \geq 3\), the author essentially shows that the empirical measure converges to the \(L^\infty\) weak solution of the aforementioned partial differential equation as the number \(N\) of particles tends to infinity for short times in the Sobolev space \(H^{s}(\mathbb{R}^d)\), for any \(s<-d/2\). In this way, we are justified in saying that, in dimensions \(d\geq 3\) (as in dimensions \(d=2\)), the proposed nonlinear scalar partial differential equation describes the dynamics of Coulomb systems when the number \(N\) of particles is very large.
Reviewer: Catalin Popa (Iaşi)Analysis of the flow of Brinkman-type nanofluid using generalized Fourier's and Fick's lawshttps://zbmath.org/1496.353262022-11-17T18:59:28.764376Z"Sheikh, Nadeem Ahmad"https://zbmath.org/authors/?q=ai:sheikh.nadeem-ahmad"Ching, Dennis Ling Chuan"https://zbmath.org/authors/?q=ai:ching.dennis-ling-chuan"bin Sakidin, Hamzah"https://zbmath.org/authors/?q=ai:bin-sakidin.hamzah"Khan, Ilyas"https://zbmath.org/authors/?q=ai:khan.ilyasBeyond Bogoliubov dynamicshttps://zbmath.org/1496.353322022-11-17T18:59:28.764376Z"Boßmann, Lea"https://zbmath.org/authors/?q=ai:bossmann.lea"Petrat, Sören"https://zbmath.org/authors/?q=ai:petrat.soren"Pickl, Peter"https://zbmath.org/authors/?q=ai:pickl.peter"Soffer, Avy"https://zbmath.org/authors/?q=ai:soffer.avrahamThe starting point of the investigations of the authors is the model describing bosons in the mean-field or Hartree regime. This is characterized by weak, long-range interactions. The authors construct a norm approximation such that all corrections to correlation functions and expectation values of bounded operators are given in terms of the two-point correlation functions of a quasifree state. The advantage of their construction that it reduces the complexity of the \(N\)-body problem and makes it possible to numerical calculate these quantities to arbitrary precision. Hence the computation of the higher-order corrections reduces to solve first the well-studied Hartree equation and second the Bogoliubov equation. The second is equivalent to solving a \(2 \times 2\) matrix differential equation. Moreover, the \(N\)-independent corrections fulfill a generalized form of Wick's theorem.
Reviewer: Ágota Figula (Debrecen)Bogoliubov theory for many-body quantum systemshttps://zbmath.org/1496.353352022-11-17T18:59:28.764376Z"Schlein, Benjamin"https://zbmath.org/authors/?q=ai:schlein.benjaminSummary: We review some recent applications of rigorous Bogoliubov theory. We show how Bogoliubov theory can be used to approximate quantum fluctuations, both in the analysis of the energy spectrum and in the study of the dynamics of many-body quantum systems.
For the entire collection see [Zbl 1465.35005].Global weak solutions for the Landau-Lifshitz-Gilbert-Vlasov-Maxwell system coupled via emergent electromagnetic fieldshttps://zbmath.org/1496.353842022-11-17T18:59:28.764376Z"Dorešić, Tvrtko"https://zbmath.org/authors/?q=ai:doresic.tvrtko"Melcher, Christof"https://zbmath.org/authors/?q=ai:melcher.christofSummary: Motivated by recent models of current driven magnetization dynamics, we examine the coupling of the Landau-Lifshitz-Gilbert equation and classical electron transport governed by the Vlasov-Maxwell system. The interaction is based on space-time gyro-coupling in the form of emergent electromagnetic fields of quantized helicity that add up to the conventional Maxwell fields. We construct global weak solutions of the coupled system in the framework of frustrated magnets with competing first- and second-order gradient interactions known to host topological solitons such as magnetic skyrmions and hopfions.On a Vlasov-Poisson system in a bounded set with direct reflection boundary conditionshttps://zbmath.org/1496.353852022-11-17T18:59:28.764376Z"Giorgi, Pierre-Antoine"https://zbmath.org/authors/?q=ai:giorgi.pierre-antoine"Nouri, Anne"https://zbmath.org/authors/?q=ai:nouri.anneSummary: The Vlasov-Poisson system models a collisionless plasma. In a bounded domain it is known that singularities can occur. Existence of global in time continuous solutions to the Vlasov-Poisson system is proven in a one-dimensional bounded domain, with direct reflection boundary conditions and initial data even with respect to the \(v\)-variable. Local in time uniqueness is proven. Generalized characteristics are used. Electroneutrality is obtained in the limit.Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibriumhttps://zbmath.org/1496.353862022-11-17T18:59:28.764376Z"Arnold, Anton"https://zbmath.org/authors/?q=ai:arnold.anton"Signorello, Beatrice"https://zbmath.org/authors/?q=ai:signorello.beatriceSummary: This paper is concerned with finding Fokker-Planck equations in \(\mathbb{R}^d\) with the fastest exponential decay towards a given equilibrium. For a prescribed, anisotropic Gaussian we determine a non-symmetric Fokker-Planck equation with linear drift that shows the highest exponential decay rate for the convergence of its solutions towards equilibrium. At the same time it has to allow for a decay estimate with a multiplicative constant arbitrarily close to its infimum. Such an ``optimal'' Fokker-Planck equation is constructed explicitly with a diffusion matrix of rank one, hence being hypocoercive. In an \(L^2\)-analysis, we find that the maximum decay rate equals the maximum eigenvalue of the inverse covariance matrix, and that the infimum of the attainable multiplicative constant is 1, corresponding to the high-rotational limit in the Fokker-Planck drift. This analysis is complemented with numerical illustrations in 2D, and it includes a case study for time-dependent coefficient matrices.From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applicationshttps://zbmath.org/1496.353922022-11-17T18:59:28.764376Z"Franceschi, J."https://zbmath.org/authors/?q=ai:franceschi.j"Pareschi, L."https://zbmath.org/authors/?q=ai:pareschi.lorenzo"Zanella, M."https://zbmath.org/authors/?q=ai:zanella.mattiaSummary: Fake news spreading, with the aim of manipulating individuals' perceptions of facts, is now recognized as a major problem in many democratic societies. Yet, to date, little has been understood about how fake news spreads on social networks, what the influence of the education level of individuals is, when fake news is effective in influencing public opinion, and what interventions might be successful in mitigating their effect. In this paper, starting from the recently introduced kinetic multi-agent model with competence by the first two authors, we propose to derive reduced-order models through the notion of social closure in the mean-field approximation that has its roots in the classical hydrodynamic closure of kinetic theory. This approach allows to obtain simplified models in which the competence and learning of the agents maintain their role in the dynamics and, at the same time, the structure of such models is more suitable to be interfaced with data-driven applications. Examples of different Twitter-based test cases are described and discussed.A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesishttps://zbmath.org/1496.353992022-11-17T18:59:28.764376Z"Roy, Souvik"https://zbmath.org/authors/?q=ai:roy.souvik.1|roy.souvik"Pan, Zui"https://zbmath.org/authors/?q=ai:pan.zui"Pal, Suvra"https://zbmath.org/authors/?q=ai:pal.suvraSummary: In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The dynamics of colon cancer is given by a Itó stochastic process, which helps in modeling the randomness present in the system. The stochastic dynamics is then represented by the Fokker-Planck (FP) partial differential equation that governs the evolution of the associated probability density function. The optimal therapies are obtained using a three step procedure. First, a finite dimensional FP-constrained optimization problem is formulated that takes input individual noisy patient data, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Next, a sensitivity analysis of the optimal parameter set is used to determine the parameters to be controlled, thus, helping in assessing the types of treatment therapies. Finally, a feedback FP control problem is solved to determine the optimal combination therapies. Numerical results with the combination drug, comprising of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed framework.Langevin approach for intrinsic fluctuations of chemical reactions with Hopf bifurcationhttps://zbmath.org/1496.370792022-11-17T18:59:28.764376Z"Xu, Hong-Yuan"https://zbmath.org/authors/?q=ai:xu.hongyuan"Luo, Yu-Pin"https://zbmath.org/authors/?q=ai:luo.yupin"Wu, Jinn-Wen"https://zbmath.org/authors/?q=ai:wu.jinnwen"Huang, Ming-Chang"https://zbmath.org/authors/?q=ai:huang.mingchangSummary: The characteristics of Langevin equations for the intrinsic fluctuations of chemical reactions are investigated via the analyses on the Brusselator model in the parameter domain of spirally stable focus. Two forms of Langevin equations are shown to be equivalent for the results of two statistical measures. The comparisons in the results of two measures between Langevin equations and chemical master equation are given: The difference in stationary probability densities is significant for systems close to the bifurcation point, even the system size is large; the power spectra of Langevin equations with white noise are qualitatively the same as that of chemical master equation, but the discrepancy is found between Langevin equations with colored noises and chemical master equation, if the length of correlation-time is comparable with the correlation-time of a system. As the linearized Langevin equations possess singularity at the supercritical Hopf bifurcation point for the statistical measures, the Langevin equations displace the bifurcation points, and the amount of displacement is a decreasing function of the system size and the length of correlation-time of noises.A \(\mathbb{Z}_2\)-topological index for quasi-free fermionshttps://zbmath.org/1496.460692022-11-17T18:59:28.764376Z"Aza, N. J. B."https://zbmath.org/authors/?q=ai:aza.n-j-b"Reyes-Lega, A. F."https://zbmath.org/authors/?q=ai:reyes-lega.andres-f"Sequera, L. A. M."https://zbmath.org/authors/?q=ai:sequera.l-a-mSummary: We use infinite dimensional self-dual CAR \(C^*\)-algebras to study a \(\mathbb{Z}_2\)-index, which classifies free-fermion systems embedded on \(\mathbb{Z}^d\) disordered lattices. Combes-Thomas estimates are pivotal to show that the \(\mathbb{Z}_2\)-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the \(\mathrm{weak}^*\)-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.Existence of minimizers for a generalized liquid drop model with fractional perimeterhttps://zbmath.org/1496.490042022-11-17T18:59:28.764376Z"Novaga, Matteo"https://zbmath.org/authors/?q=ai:novaga.matteo"Onoue, Fumihiko"https://zbmath.org/authors/?q=ai:onoue.fumihikoSummary: We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop model. We first show the existence of minimizers for any volumes if the kernel of the Riesz potential decays faster than that of the fractional perimeter. We also prove the existence of generalized minimizers for any volumes if the kernel of the Riesz potential just vanishes at infinity. Finally, we study the asymptotic behavior of minimizers when the volume goes to infinity and we prove that a sequence of minimizers converges to the Euclidean ball up to translations if the kernel of the Riesz potential decays sufficiently fast.Knot theory and statistical mechanicshttps://zbmath.org/1496.570012022-11-17T18:59:28.764376Z"Kauffman, Louis H."https://zbmath.org/authors/?q=ai:kauffman.louis-hirschSummary: This chapter discusses connections between knot theory and statistical mechanics and quantum amplitudes.
For the entire collection see [Zbl 1491.46002].Counting the zeros of an elephant random walkhttps://zbmath.org/1496.600862022-11-17T18:59:28.764376Z"Bertoin, Jean"https://zbmath.org/authors/?q=ai:bertoin.jeanThe elephant random walk (ERW) can be viewed as a member of the family of reinforced processes (see [\textit{G. M. Schütz} and \textit{S. Trimper}, ``Elephants can always remember: exact long-range memory effects in a non-Markovian random walk'', Phys. Rev. E 70, No. 4, Article ID045101, 4 p. (2004; \url{doi:10.1103/PhysRevE.70.045101})]). The present paper studies how memory impacts passages at the origin for a ERW in the diffusive regime. It is shown that the number of zeros always grows asymptotically like the square root of the time. The problem is that, depending on the memory parameter, first return times to 0 may have a finite expectation or a fat tail with exponent less than 1/2. The author solves this problem by recasting the questions in the framework of scaling limits for self-similar Markov processes and for Markov chains.
Reviewer: Anatoliy Swishchuk (Calgary)Refined large deviation principle for branching Brownian motion conditioned to have a low maximumhttps://zbmath.org/1496.601042022-11-17T18:59:28.764376Z"Bai, Yanjia"https://zbmath.org/authors/?q=ai:bai.yanjia"Hartung, Lisa"https://zbmath.org/authors/?q=ai:hartung.lisa-barbelA binary branching Brownian motion is a particle system on the real line starting from a unique particle at position \(0\) at time \(0\), in which particle move according to independent Brownian motions, and split at rate \(1\) into two particles. Denote by \(\tau\) the first branching time, by \(y\) the position of the initial particle at that first branching time and by \(M_t\) the rightmost occupied position at time \(t\). It is well known that in this process, one has \(\lim_{t \to \infty} \frac{M_t}{t}=\sqrt{2}\) almost surely. The present article studies the behaviour of the branching Brownian motion conditioned on the large deviation event \(\{M_t<\sqrt{2}\alpha t\}\) for \(\alpha < 1\).
The large deviations for the maximal displacement of the branching Brownian motion were studied in [\textit{B. Derrida} and \textit{Z. Shi}, Springer Proc. Math. Stat. 208, 303--312 (2017; Zbl 1386.60290)], in which it is observed that conditioning the maximum to be small has the effect of suppressing the branching of the process for a positive proportion of the time and changing the speed of the initial particle. In the present article, the authors give precise estimates on the position and time of first branching of a branching Brownian motion conditioned on \(\{M_t<\sqrt{2}\alpha t\}\), obtaining a large deviations estimates for the couple \((\tau,y)\). The large deviations functional of this pair of variables exhibits a number of first and second order phase transitions.
Reviewer: Bastien Mallein (Paris)Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscapehttps://zbmath.org/1496.601152022-11-17T18:59:28.764376Z"Bates, Erik"https://zbmath.org/authors/?q=ai:bates.erik"Ganguly, Shirshendu"https://zbmath.org/authors/?q=ai:ganguly.shirshendu"Hammond, Alan"https://zbmath.org/authors/?q=ai:hammond.alanSummary: Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work [``The directed landscape'', Preprint, \url{arXiv:1812.00309}] of \textit{D. Dauvergne} et al., this object was constructed and, upon a parabolic correction, shown to be the limit of one such model: Brownian last passage percolation. The limit object without parabolic correction, called the directed landscape, admits geodesic paths between any two space-time points \((x,s)\) and \((y,t)\) with \(s< t\). In this article, we examine fractal properties of the set of these paths. Our main results concern exceptional endpoints admitting disjoint geodesics. First, we fix two distinct starting locations \(x_1\) and \(x_2\), and consider geodesics traveling \((x_1, 0)\to (y,1)\) and \((x_2, 0)\to (y,1)\). We prove that the set of \(y\in \mathbb{R}\) for which these geodesics coalesce only at time 1 has Hausdorff dimension one-half. Second, we consider endpoints \((x,0)\) and \((y,1)\) between which there exist two geodesics intersecting only at times 0 and 1. We prove that the set of such \((x,y)\in\mathbb{R}^2\) also has Hausdorff dimension one-half. The proofs require several inputs of independent interest, including (i) connections to the so-called \textit{difference weight profile} studied in
[\textit{R. Basu} et al., Ann. Probab. 49, No. 1, 485--505 (2021; Zbl 1457.82165)]; and (ii) a tail estimate on the number of disjoint geodesics starting and ending in small intervals. The latter result extends the analogous estimate proved for the prelimiting model in [\textit{A. Hammond}, Proc. Lond. Math. Soc. (3) 120, No. 3, 370--433 (2020; Zbl 1453.82078)].The logarithmic anti-derivative of the baik-rains distribution satisfies the KP equationhttps://zbmath.org/1496.601182022-11-17T18:59:28.764376Z"Zhang, Xincheng"https://zbmath.org/authors/?q=ai:zhang.xinchengSummary: It has been discovered that the Kadomtsev-Petviashvili (KP) equation governs the distribution of the fluctuation of many random growth models. In particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP equation. We prove that the anti-derivative of the Baik-Rains distribution, which governs the fluctuation of the models in the KPZ universality class starting with stationary initial data, satisfies the KP equation. The result is first derived formally by taking a limit of the generating function of the KPZ equation, which satisfies the KP equation. Then we prove it directly using the explicit Painlevé II formulation of the Baik-Rains distribution.On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient modelhttps://zbmath.org/1496.740242022-11-17T18:59:28.764376Z"Wang, Binying"https://zbmath.org/authors/?q=ai:wang.binying"Liu, Jinxing"https://zbmath.org/authors/?q=ai:liu.jinxing"Soh, A. K."https://zbmath.org/authors/?q=ai:soh.ai-kah"Liang, Naigang"https://zbmath.org/authors/?q=ai:liang.naigang(no abstract)Thermodynamical analysis of hysteresis in rigid ferroelectric bodies ZAMP-D-21-00505R1https://zbmath.org/1496.740522022-11-17T18:59:28.764376Z"Alhasadi, Mawafag F."https://zbmath.org/authors/?q=ai:alhasadi.mawafag-f"Ghansela, Pankaj"https://zbmath.org/authors/?q=ai:ghansela.pankaj"Sun, Qiao"https://zbmath.org/authors/?q=ai:sun.qiao"Federico, Salvatore"https://zbmath.org/authors/?q=ai:federico.salvatore.1Summary: We propose a nonlinear thermoelectric framework adequate for capturing the phenomenon of electrical hysteresis in ferroelectric materials. We call this formulation \textit{rate-independent ferroelectricity}, because the rate of polarisation is linear in the rate of the electric field, so that the process is independent of the time scale. This is inspired by the theory of rate-independent plasticity in the early form proposed by \textit{A. E. Green} and \textit{P. M. Naghdi} [Arch. Ration. Mech. Anal. 18, 251--281 (1965; Zbl 0133.17701)] and
\textit{J. Kratochvil} and \textit{O. W. Dillon Jr.} [``Thermodynamics of elastic-plastic materials as a theory with internal state variables'', J. Appl. Phys. 40, No. 8, 3207--3218 (1969; \url{doi:10.1063/1.1658167})], whose works were in turn based on the formulation of thermodynamics with internal variables by
\textit{B: D. Coleman} and \textit{M. E. Gurtin} [``Thermodynamics with internal state variables'', J. Chem. Phys. 47, 597--613 (1967; \url{doi:10.1063/1.1711937})]. We impose thermodynamical restrictions on the proposed constitutive equations in order to guarantee positive dissipation under irreversible switching (domain switching). Finally, we illustrate the proposed framework with the numerical solution of a one-dimensional example, in which a cyclic electric field is applied, resulting in a ferroelectric polarisation-electric field hysteresis loop. The novelty of this work is in the use of an analogue of the evolution law proposed by Green and Naghdi [loc. cit.] to simulate the electrical hysteresis behaviour in ferroelectric materials, caused by domain wall motion under cyclic electric loadings. This hysteresis loop eventually results in a significant residual electric polarisation.Reflection phenomena of waves in a semiconductor nanostructure elasticity mediumhttps://zbmath.org/1496.740812022-11-17T18:59:28.764376Z"Adnan, J."https://zbmath.org/authors/?q=ai:adnan.j"Ali, Hashmat"https://zbmath.org/authors/?q=ai:ali.hashmat"Khan, Aftab"https://zbmath.org/authors/?q=ai:khan.aftab(no abstract)An introduction to quantum fluidshttps://zbmath.org/1496.760052022-11-17T18:59:28.764376Z"Dinh, Phuong Mai"https://zbmath.org/authors/?q=ai:dinh.phuong-mai"Navarro, Jesús"https://zbmath.org/authors/?q=ai:navarro.jesus-gerardo"Suraud, Éric"https://zbmath.org/authors/?q=ai:suraud.ericPublisher's description: What do atomic nuclei, neutron stars, a domestic power supply, and the stunning colors of stained glass in cathedrals all have in common? The answer lies in the unifying concept of quantum fluids, which allows us to understand the behavior and properties of these different systems in simple terms. This book reveals how quantum mechanics, usually considered as restricted to the invisible microscopic world, in fact plays a crucial role at all scales of the universe. The purpose of the book is to introduce the reader to the fascinating and multifaceted world of quantum fluids, which covers different systems at different scales in the physical world.
The first part of the book discusses the notion of phases (solid, liquid, gas), presents basic aspects of the structure of matter and quantum mechanics, and includes some elements of statistical mechanics. The second part provides a description of the major quantum liquids, starting with the paramount case of electron fluids and their many applications in everyday life, followed by liquid helium and atomic nuclei. The authors go on to explore matter at very high densities, covering nuclear matter and compact stars, and the behavior of matter at extremely low temperatures, with the fascinating `superphases' of superconductivity and superfluidity.
The topic of quantum fluids has multidisciplinary applications and this book will appeal to students and researchers in physics, chemistry, astrophysics, engineering and materials science.A gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinateshttps://zbmath.org/1496.761052022-11-17T18:59:28.764376Z"Wang, Yi"https://zbmath.org/authors/?q=ai:wang.yi.2|wang.yi.5|wang.yi.6|wang.yi.9|wang.yi.8|wang.yi.7|wang.yi.1|wang.yi.4|wang.yi.3"Zhang, Jiexing"https://zbmath.org/authors/?q=ai:zhang.jiexing"Ni, Guoxi"https://zbmath.org/authors/?q=ai:ni.guoxiSummary: Many configurations in plasma physics are axisymmetric, it will be more convenient to depict them in cylindrical coordinates compared with Cartesian coordinates. In this paper, a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed, our algorithm is based on Strang splitting. The equation is divided into two parts, one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme, and the other is the acceleration part solved by a Runge-Kutta solver. The asymptotic preserving property of whole algorithm is proved and it's applied on the study of charge separation problem in plasma edge and 1D Z-pinch configuration. Numerical results show it can capture the process from non-equilibrium to equilibrium state by Coulomb collisions, and numerical accuracy is obtained.Erratum to: ``On the entropic property of the ellipsoidal statistical model with the Prandtl number below 2/3''https://zbmath.org/1496.761202022-11-17T18:59:28.764376Z"Takata, Shigeru"https://zbmath.org/authors/?q=ai:takata.shigeru"Hattori, Masanari"https://zbmath.org/authors/?q=ai:hattori.masanari"Miyauchi, Takumu"https://zbmath.org/authors/?q=ai:miyauchi.takumuErratum to the authors' paper [ibid. 13, No. 6, 1163--1174 (2020; Zbl 1453.76197)].Electronic circuit simulation and the development of new Krylov-subspace methodshttps://zbmath.org/1496.780042022-11-17T18:59:28.764376Z"Freund, Roland W."https://zbmath.org/authors/?q=ai:freund.roland-wSummary: Ever since the 1960s, the semiconductor industry has heavily relied on simulation in order to analyze and verify the design of integrated circuits before actual chips are manufactured. Over the decades, the algorithms and tools of circuit simulation have evolved in order to keep up with the ever-increasing complexity of integrated circuits, and at certain points of this evolution, new simulation techniques were required. Such a point was reached in the early 1990s, when a new approach was needed to efficiently and accurately simulate the effects of the ever-increasing amount of on-chip wiring on the proper functioning of the chip. The industry's proposed solution for this task, the AWE approach, worked well for small- to moderate-size networks of on-chip wiring, but suffered from numerical issues for larger networks. It turned out that for the special case of networks with single inputs and single outputs, these problems can be remedied by exploiting the connection between AWE and the classical Lanczos algorithm for single starting vectors. However, the general case of on-chip wiring involves networks with multiple inputs and outputs, and so a Lanczostype algorithm was needed that could handle such multiple starting vectors. Since no such extension existed, a new band Lanczos algorithm for multiple starting vectors was developed. It turned out that this new band approach can also be employed to devise extensions of other Krylov-subspace methods. In this chapter, we describe the band Lanczos algorithm and the band Arnoldi process and how their developments were driven by the need to efficiently and accurately simulate the effects of on-chip wiring of integrated circuits.
For the entire collection see [Zbl 1483.65008].Nonlinear dynamic modeling for high temperature superconductivity in nanocluster topological structures on solid surfacehttps://zbmath.org/1496.780122022-11-17T18:59:28.764376Z"Arakelian, Sergei M."https://zbmath.org/authors/?q=ai:arakelian.sergei-m"Chestnov, Igor Yu."https://zbmath.org/authors/?q=ai:chestnov.igor-yu"Istratov, Alexander V."https://zbmath.org/authors/?q=ai:istratov.alexander-v"Khudaiberganov, Timur A."https://zbmath.org/authors/?q=ai:khudaiberganov.timur-a"Butkovskiy, Oleg Ya."https://zbmath.org/authors/?q=ai:butkovskii.oleg-yaroslavovichSummary: We studied laser-induced nanocluster structures of different types in both topology and the element compositions due to the nonlinear interaction of laser radiation with the condensed matter taking into account the correlations in nanoparticle ensemble by quantum states. The problem of both optical response and high temperature superconductivity, due to topological surface structures with correlated states, is under our consideration in the frame of nonlinear dynamic modeling resulting, e.g., in the electronic Cooper pairs appearance. Random temporal and spatial variations in selected topological parameters may result in large variations of such functional properties. The analogy with nonlinear dynamics of system under external noise takes place in the case. Quantum mobility of electrons over different trajectories in the spatially inhomogeneous structures/nanocluster systems is presented in accordance with the path integral-theory approach.
For the entire collection see [Zbl 1470.74004].Nonlinear dynamic processes in laser-induced transitions to low-dimensional carbon nanostructures in bulk graphite unithttps://zbmath.org/1496.780142022-11-17T18:59:28.764376Z"Khorkov, Kirill"https://zbmath.org/authors/?q=ai:khorkov.kirill"Kochuev, Dmitriy"https://zbmath.org/authors/?q=ai:kochuev.dmitriy"Chkalov, Ruslan"https://zbmath.org/authors/?q=ai:chkalov.ruslan"Prokoshev, Valery"https://zbmath.org/authors/?q=ai:prokoshev.valery"Arakelian, Sergei"https://zbmath.org/authors/?q=ai:arakelian.sergei-mSummary: Development of nonstationary technique for the laser-induced functional elements synthesis based on micro- and nanostructures in graphite samples is under study. Carbon nanostructures such as graphene, nanopeaks, and crystals have been obtained in our experiments. The nonlinear formation mechanisms of nanostructures and microcrystals under femtosecond laser radiation for graphite in liquid nitrogen are analyzed. Femtosecond laser pulses with high power allow achieving the local transient conditions for the nonstationary material processing resulting in ablation, sufficient modification of the structure, and/or changing of the phase composition of the materials. Liquid nitrogen as a cryogenic and/or reaction liquid contributes to additional fast cooling and stabilization of the fabricated micro- and nanostructures.
For the entire collection see [Zbl 1470.74004].Quantum entanglement of Bosonic Josephson junctions in weak population limithttps://zbmath.org/1496.810352022-11-17T18:59:28.764376Z"Li, Song-Song"https://zbmath.org/authors/?q=ai:li.songsongSummary: We investigate the entanglement behavior of two boson ensembles in weak population limit. We first obtain the analytical expressions of the wave function and the entanglement parameter. By numerically calculate entanglement parameter, we see that the better entanglement can be achieved by enhancing the nonlinearity, the coherent coupling and decreasing the interspecies interaction.Bound state solutions and thermodynamic properties of modified exponential screened plus Yukawa potentialhttps://zbmath.org/1496.810482022-11-17T18:59:28.764376Z"Antia, Akaninyene D."https://zbmath.org/authors/?q=ai:antia.akaninyene-d"Okon, Ituen B."https://zbmath.org/authors/?q=ai:okon.ituen-b"Isonguyo, Cecilia N."https://zbmath.org/authors/?q=ai:isonguyo.cecilia-n"Akankpo, Akaninyene O."https://zbmath.org/authors/?q=ai:akankpo.akaninyene-o"Eyo, Nsemeke E."https://zbmath.org/authors/?q=ai:eyo.nsemeke-eSummary: In this research paper, the approximate bound state solutions and thermodynamic properties of Schrödinger equation with modified exponential screened plus Yukawa potential (MESPYP) were obtained with the help Greene-Aldrich approximation to evaluate the centrifugal term. The Nikiforov-Uvarov (NU) method was used to obtain the analytical solutions. The numerical bound state solutions of five selected diatomic molecules, namely mercury hydride (HgH), zinc hydride (ZnH), cadmium hydride (CdH), hydrogen bromide (HBr) and hydrogen fluoride (HF) molecules were also obtained. We obtained the energy eigenvalues for these molecules using the resulting energy eigenequation and total unnormalized wave function expressed in terms of associated Jacobi polynomial. The resulting energy eigenequation was presented in a closed form and applied to study partition function (Z) and other thermodynamic properties of the system such as vibrational mean energy (U), vibrational specific heat capacity (C), vibrational entropy (S) and vibrational free energy (F). The numerical bound state solutions were obtained from the resulting energy eigenequation for some orbital angular quantum number. The results obtained from the thermodynamic properties are in excellent agreement with the existing literature. All numerical computations were carried out using spectroscopic constants of the selected diatomic molecules with the help of MATLAB 10.0 version. The numerical bound state solutions obtained increases with an increase in quantum state.Time reversal symmetry for classical, non-relativistic quantum and spin systems in presence of magnetic fieldshttps://zbmath.org/1496.810492022-11-17T18:59:28.764376Z"Carbone, Davide"https://zbmath.org/authors/?q=ai:carbone.davide"De Gregorio, Paolo"https://zbmath.org/authors/?q=ai:de-gregorio.paolo"Rondoni, Lamberto"https://zbmath.org/authors/?q=ai:rondoni.lambertoSummary: We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations and the so-called fluctuation theorems, are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are non-relativistic, and are described by the Schrödinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases. These results are relevant for experiments such as diffusion in solutions, thermoelectricity and spin charge transport. Indeed, no violation of the Onsager relations has been found in presence of a magnetic field, contrary to general expectations.Evolution of energy and magnetic moment of a quantum charged particle in power-decaying magnetic fieldshttps://zbmath.org/1496.810522022-11-17T18:59:28.764376Z"Dodonov, V. V."https://zbmath.org/authors/?q=ai:dodonov.victor-v"Horovits, M. B."https://zbmath.org/authors/?q=ai:horovits.m-bSummary: We consider a quantum spinless nonrelativistic charged particle moving in the \(xy\) plane under the action of a homogeneous time-dependent magnetic field \(B(t) = B_0(1 + t/t_0)^{-1-g}\), directed along the \(z\)-axis and described by means of the vector potential \(\mathbf{A}(t) = B(t)[-y, x]/2\). Assuming that the particle was initially in the thermal equilibrium state with a negligible coupling to a reservoir, we obtain exact formulas for the time-dependent mean values of the energy and magnetic moment in terms of the Bessel functions. Different regimes of the evolution are discovered and illustrated in several figures. The energy goes asymptotically to a finite value if \(g > 0\) (``fast'' decay), while it goes asymptotically to zero if \(g \leq 0\) (``slow'' decay). The dependence on parameter \(t_0\) practically disappears when \(1 + g\) is close to zero value (``superslow'' decay). The mean magnetic moment goes to zero for \(g > 1\), while it grows unlimitedly if \(g < 1\).Factoring discrete-time quantum walks on distance regular graphs into continuous-time quantum walkshttps://zbmath.org/1496.810612022-11-17T18:59:28.764376Z"Zhan, Hanmeng"https://zbmath.org/authors/?q=ai:zhan.hanmengSummary: We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph \(X\). Given that \(X\) has diameter \(d\) and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on \(X\) is a product of at most \(d\) commuting transition matrices of continuous-time quantum walks, each on some distance digraph of the line digraph of \(X\). We also obtain a similar factorization for any graph \(X\) in a Bose Mesner algebra.Photovoltaic efficiency at maximum power of a quantum dot moleculehttps://zbmath.org/1496.810622022-11-17T18:59:28.764376Z"Lira, J."https://zbmath.org/authors/?q=ai:lira.jaroslaw|lira.jorge-h-s"Sanz, L."https://zbmath.org/authors/?q=ai:sanz.l-m|sanz.luis|sanz.leon"Alcalde, A. M."https://zbmath.org/authors/?q=ai:alcalde.a-mSummary: In this work, the behavior of the efficiency at the maximum power of a quantum dot molecule, acting as a device for photovoltaic conversion, is investigated. A theoretical approach using a master equation, considering the effect of the energy offsets, and the width of the quantum barrier, identify realistic physical conditions that enhance the photovoltaic response of the photocell. By mapping the effect of the control of the energy offsets of the nanostructure, a condition for gain in 30\% of maximum power delivered per molecule if compared with a single quantum dot is demonstrated. Studying the behavior as a function of temperature, the physical system exhibits gain when compared to the Chambadal-Novikov-Curzon-Ahlborn efficiency at maximum power, without exceeding Carnot's efficiency, as expected from the second law of thermodynamics.Wigner function as a detector of entanglement in open two coupled Inas semiconductor quantum dotshttps://zbmath.org/1496.810632022-11-17T18:59:28.764376Z"Mansour, H. Ait"https://zbmath.org/authors/?q=ai:mansour.hicham-ait"Siyouri, F-Z."https://zbmath.org/authors/?q=ai:siyouri.f-zSummary: We tested the ability of Wigner function to reveal and capture the quantum entanglement presents in two coupled semiconductor InAs quantum dots that independently interact with dephasing reservoirs. In this respect, we analyze their evolution against the temperature parameter as well as against the dimensionless time in both Markovian and non-Markovian environments. Further, we compare their amounts and their behaviors under the Förster interaction effect. In particular, we show that for large values of dimensionless time and at higher temperature, unlike the full disappear of entanglement the positive part of Wigner function still survives. Moreover, we show that the Wigner function volume is influenced by the variation of the Förster interaction, the temperature and the non-Markovianity degree. Nevertheless, its ability to reveal the quantum entanglement presents inside two coupled semiconductor quantum dots is still kept.The properties of the polaron in III-V compound semiconductor quantum dots induced by the influence of Rashba spin-orbit interactionhttps://zbmath.org/1496.810642022-11-17T18:59:28.764376Z"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.61"Han, Shuang"https://zbmath.org/authors/?q=ai:han.shuang"Ma, Xin-Jun"https://zbmath.org/authors/?q=ai:ma.xinjun"Xianglian"https://zbmath.org/authors/?q=ai:xianglian."Sun, Yong"https://zbmath.org/authors/?q=ai:sun.yong"Xiao, Jing-Lin"https://zbmath.org/authors/?q=ai:xiao.jinglinSummary: We study the ground state energy (GSE) of weak coupling polaron confined in quantum dots (QD) of III-V compound semiconductors using the linear combinatorial operator (LCO) and the Lee-Low-Pines unitary transformation (LLPUT) method. Our calculated results show that the GSE of the polaron splits into two branches due to the Rashba spin-orbit (SO) coupling effect, and spin splitting spacing is influenced by Rashba SO coupling strength and the coupling strength and the effective mass of III-V compound semiconductor material. That reveals the SO coupling properties of weak coupling polaron in the QD of III-V compound semiconductors, which provides a theoretical platform for the fabrication of nanometer devices.Quantum-memory-assisted entropic uncertainty relation in the Heisenberg XXZ spin chain model with external magnetic fields and Dzyaloshinski-Moriya interactionhttps://zbmath.org/1496.810702022-11-17T18:59:28.764376Z"Zhang, Yanliang"https://zbmath.org/authors/?q=ai:zhang.yanliang"Zhou, Qingping"https://zbmath.org/authors/?q=ai:zhou.qingping"Kang, Guodong"https://zbmath.org/authors/?q=ai:kang.guodong"Wen, Jiaxin"https://zbmath.org/authors/?q=ai:wen.jiaxin"Fang, Maofa"https://zbmath.org/authors/?q=ai:fang.maofaSummary: In this paper, we investigate the quantum-memory-assisted (QMA) entropic uncertainty relation in the two-qubit Heisenberg XXZ spin chain model. The contributions of relevant parameters of the model on the reducing of QMA entropic uncertainty concerning a pair of Pauli observables are studied in detail under the thermal equilibrium and intrinsic decoherence conditions, respectively. The results show that, in the case of thermal equilibrium, the lower of \(T\) and the stronger of spin coupling interaction \(J,J_z\) and Dzyaloshinskii-Moriya (DM) interaction \(D_z\) are more beneficial to the reducing of QMA entropic uncertainty. However, the stronger of external nonuniform magnetic field \(\mathfrak{B}\) hinders the reducing of the QMA entropic uncertainty. Meanwhile, there exists a critical phenomena with respect to \(\mathfrak{B}\) at the extremal low temperature. By taking into account the effect of intrinsic decoherence, it is found that the dynamical features of QMA entropic uncertainty are sensitive to the values of \(D_z\) and unnonuniform magnetic fields \(\mathfrak{b}\). In the weak DM interaction region, the strengthening of \(D_z\) can markedly reduce the entropic uncertainty \(U\) during the evolution process, but, in the strong DM interaction region, the strengthening of \(D_z\) makes the effect of intrinsic decoherence more pronounced. Furthermore, the large nonuniformity \(\mathfrak{b}\) dose not suppress the entropic uncertainty but makes the oscillation behaviours of \(U\) and \(U_b\) disappear. The large nonuniformity \(\mathfrak{b}\) also makes the effect of intrinsic decoherence more pronounced.Explosive synchronization induced by environmental couplinghttps://zbmath.org/1496.810742022-11-17T18:59:28.764376Z"Ramesan, Gayathri"https://zbmath.org/authors/?q=ai:ramesan.gayathri"Shajan, Emilda"https://zbmath.org/authors/?q=ai:shajan.emilda"Shrimali, Manish Dev"https://zbmath.org/authors/?q=ai:shrimali.manish-devSummary: The occurrence of explosive synchronization transition in a system of limit-cycle oscillators in the presence of two types of coupling; direct mean field diffusive and indirect environmental couplings, both operating simultaneously, is reported. The dynamics of coupled nonlinear Van der Pol and Rayleigh oscillators are studied in detail as a function of the distribution of intrinsic parameters of the oscillators. This explosive synchronization transition depends on the strength of indirect coupling and is irreversible giving rise to a characteristic hysteresis region. The different routes to synchronization observed in these coupled oscillators are studied in detail with the help of effective frequency and time series analysis. We have investigated the efficiency of the proposed scheme in various other topologies such as random, scale-free, and two-community networks as well.Transport properties of a 3-dimensional holographic effective theory with gauge-axion couplinghttps://zbmath.org/1496.810872022-11-17T18:59:28.764376Z"Li, Yi-Lin"https://zbmath.org/authors/?q=ai:li.yilin"Wang, Xi-Jing"https://zbmath.org/authors/?q=ai:wang.xi-jing"Fu, Guoyang"https://zbmath.org/authors/?q=ai:fu.guoyang"Wu, Jian-Pin"https://zbmath.org/authors/?q=ai:wu.jian-pinSummary: In this paper, we implement a 3-dimensional holographic effective theory with gauge-axion coupling. The analytical black hole solution is worked out. We investigate the Direct current (DC) thermoelectric conductivities. A novel property is that DC electric conductivity for vanishing gauge-axion coupling is temperature dependent. It is different from that of 4-dimensional axion model whose DC electric conductivity is temperature independent. In addition, the gauge-axion coupling induces a metal insulator transition (MIT) at zero temperature. The properties of other DC thermoelectric conductivities are also discussed. Moreover we find that the Wiedemann-Franz (WF) law is violated in our model.Muon \(g - 2\) anomaly and non-localityhttps://zbmath.org/1496.810992022-11-17T18:59:28.764376Z"Capolupo, A."https://zbmath.org/authors/?q=ai:capolupo.antonio"Lambiase, G."https://zbmath.org/authors/?q=ai:lambiase.gaetano"Quaranta, A."https://zbmath.org/authors/?q=ai:quaranta.antonella|quaranta.anna-graziaSummary: We show that the discrepancy between the observed value of the muon anomalous moment and the standard model prediction can be explained in the framework of nonlocal theories. We compute the leading order and next to leading order nonlocal correction to the anomalous magnetic moment \(\alpha_{NL}\) and we find that it depends on the nonlocality scale \(M_f\) and the fermion mass \(m_f\) as \(\alpha_{NL} \propto \frac{m_f^2}{M_f^2}\). Such a dependence of the anomalous magnetic moment allows to explain, in a flavor-blind nonlocality scale, why the observed anomalous magnetic moment of the electron is much closer to the standard model prediction, and permits to predict a large anomaly that should exist for the \(\tau\) particle. We also determine the lower bounds on the nonlocality scale, for both flavor-blind and flavor-dependent scenarios.(2+1)-dimensional unstable matter waves in self-interacting Pseudospin-1/2 BECs under combined Rashba and Dresselhaus spin-orbit couplingshttps://zbmath.org/1496.811092022-11-17T18:59:28.764376Z"Tabi, Conrad Bertrand"https://zbmath.org/authors/?q=ai:tabi.conrad-bertrand"Veni, Saravana"https://zbmath.org/authors/?q=ai:veni.saravana"Kofané, Timoléon Crépin"https://zbmath.org/authors/?q=ai:kofane.timoleon-crepinSummary: The modulational instability (MI) of continuous waves is exclusively addressed theoretically and numerically in a two-component Bose-Einstein condensate in the presence of a mixture of Rashba and Dresselhaus (RD) spin-orbit couplings and the Lee-Huang-Yang (LHY) term. The linear stability analysis is utilized to derive an expression for the MI growth rate. It is revealed that instability can be excited in the presence of the RD spin-orbit coupling under conditions where nonlinear and dispersive effects are suitably balanced. Analytical predictions are confirmed via direct numerical simulations, where MI is manifested by the emergence of soliton-molecules that include four-peaked solitons and more exotic vortex structures that are very sensitive to variations in spin-orbit coupling strengths. Our study suggests that MI is a suitable mechanism for generating matter waves through multi-peaked solitons of various geometries.Statistical physics. From thermodynamics to quantum statics through five postulateshttps://zbmath.org/1496.820012022-11-17T18:59:28.764376Z"van Dongen, Peter"https://zbmath.org/authors/?q=ai:van-dongen.peterPublisher's description: Dieses Lehrbuch verfolgt das didaktische Ziel, die Statistische Physik einerseits methodisch sorgfältig darzustellen und andererseits Studierenden anhand von vielfältigen Beispielen die weitreichenden Anwendungsmöglichkeiten dieses Faches zu demonstrieren. Dazu werden bei den Herleitungen die verwendeten physikalischen Argumente ausführlich erläutert, sowie die mathematischen Berechnungen schrittweise begründet und leicht nachvollziehbar dargestellt. Zahlreiche Aufgaben mit vollständigen Lösungen, die einen effizienten Lösungsweg aufzeigen und auch die physikalische Interpretation der Ergebnisse enthalten, unterstützen die Studierenden bei der eigenständigen Beschäftigung mit dem Stoff. Die Darstellung geht von klar definierten Ausgangspunkten (den Postulaten) aus und führt möglichst effektiv und transparent von den Grundsätzen über die Ensembletheorie zu den Anwendungen. Generell wird die quantenmechanische Natur der Realität ernst genommen, ohne jedoch die Diskussion der klassischen Grenzfälle zu vernachlässigen. Das Buch ist modular aufgebaut und methodisch kohärent. Es präsentiert die ``Statistische Physik,'' die Studierende der Physik und verwandter Fächer typischerweise während ihres Bachelor-Studiums in Theorievorlesungen hören. Dadurch eignet es sich ausgezeichnet sowohl als flexibles Begleitbuch zu Vorlesungen auf verschiedenem Niveau als auch zum Selbststudium.On the hydrodynamic behaviour of a particle system with nearest neighbour interactionshttps://zbmath.org/1496.820022022-11-17T18:59:28.764376Z"Dalinger, Alexander"https://zbmath.org/authors/?q=ai:dalinger.alexanderSummary: In this thesis we will study a system of Brownian particles on the real line, which
are coupled through the nearest neighbours by an attractive potential. This model is
related to the Ginzburg-Landau model. We will prove two results. The first result is
the hydrodynamic equation for the particle density. More precisely, we show that the
empirical measure of the particle positions converges in the hydrodynamic limit to a
deterministic and absolutely continuous probability measure, where the density solves
a nonlinear heat equation. The crucial idea will be the reduction of the particle model
to the height model, in the literature also called Ginzburg-Landau interface model. We
will obtain the claimed result by taking the limit in the height model and passing back
to the particle model. Further, we will outline how this approach generalises to multiple
dimensions. The second result is the characterisation of the equilibrium fluctuations in
the case of quadratic potential. We will consider the fluctuation field, which is defined as
the square root of the number of particles times the difference of the empirical measure
of the particle positions and its expectation. Assuming the initial distribution of the
particle system to be stationary, we will show that the fluctuation field converges in the
hydrodynamic limit to an infinite-dimensional Ornstein-Uhlenbeck process. The proof
will consist of characterising the accumulation points of the distributions of fluctuation
fields by means of a martingale problem and showing tightness.Symmetry-resolved entanglement entropy in critical free-fermion chainshttps://zbmath.org/1496.820032022-11-17T18:59:28.764376Z"Jones, Nick G."https://zbmath.org/authors/?q=ai:jones.nick-gThe entanglement entropy, defined using the reduced density matrix of a multipartite quantum state, plays an important role in understanding the nature of quantum states. For quantum systems with a symmetry, the reduced density matrix can be further projected into the sectors with different symmetry charges to define the so-called symmetry-resolved entanglement entropy for each symmetry sector.
This paper calculates the symmetry-resolved Rényi entanglement entropy of \(L\) consecutive sites in a family of critical free fermionic chains with U(1) symmetry (particle-number conservation). These lattice models have a low-energy effective theory given by \(N\) massless Dirac fermions. The calculation of the symmetry-resolved entanglement entropy is performed by considering the large \(L\) asymptotic expansion of the charged moments of the reduced density matrix, whose Fourier transform gives the symmetry-resolved Rényi entropies. Using Toeplitz determinant theory, the leading and subleading terms of the charged moments are calculated and compared with conformal field theory results. A particular emphasis is given to the analysis of the subleading correction, where the discrepancy in an error term is discussed and open issues are pointed out.
Reviewer: Hong-Hao Tu (Dresden)1D three-state mean-field Potts model with first- and second-order phase transitionshttps://zbmath.org/1496.820042022-11-17T18:59:28.764376Z"Ostilli, Massimo"https://zbmath.org/authors/?q=ai:ostilli.massimo"Mukhamedov, Farrukh"https://zbmath.org/authors/?q=ai:mukhamedov.farruh-mSummary: We analyze a three-state Potts model built over a lattice ring, with coupling \(J_0\), and the fully connected graph, with coupling \(J\). This model is effectively mean-field and can be exactly solved by using transfer-matrix method and Cardano formula. When \(J\) and \(J_0\) are both ferromagnetic, the model has a first-order phase transition which turns out to be a smooth modification of the known phase transition of the traditional mean-field Potts model (\(J_0 = 0\)), despite, as we prove, the connected correlation functions are now non zero, even in the paramagnetic phase. Furthermore, besides the first-order transition, there exists also a hidden continuous transition at a temperature below which the symmetric metastable state ceases to exist. When \(J\) is ferromagnetic and \(J_0\) antiferromagnetic, a similar antiferromagnetic counterpart phase transition scenario applies. Quite interestingly, differently from the Ising-like two-state case, for large values of the antiferromagnetic coupling \(J_0\), the critical temperature of the system tends to a finite value. Similarly, also the latent heat per spin tends to a finite constant in the limit of \(J_0 \to -\infty\).Correlation decay for hard spheres via Markov chainshttps://zbmath.org/1496.820052022-11-17T18:59:28.764376Z"Helmuth, Tyler"https://zbmath.org/authors/?q=ai:helmuth.tyler"Perkins, Will"https://zbmath.org/authors/?q=ai:perkins.will"Petti, Samantha"https://zbmath.org/authors/?q=ai:petti.samanthaSummary: We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions three and higher. As the dimension tends to infinity, our improvements are by factors of 2 and 1.7, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and temporal mixing for hard spheres to deduce our results.Dropleton-soliton crossover mediated via trap modulationhttps://zbmath.org/1496.820062022-11-17T18:59:28.764376Z"Debnath, Argha"https://zbmath.org/authors/?q=ai:debnath.argha"Khan, Ayan"https://zbmath.org/authors/?q=ai:khan.ayan"Basu, Saurabh"https://zbmath.org/authors/?q=ai:basu.saurabhSummary: We report a droplet to a soliton crossover by tuning the external confinement potential in a dilute Bose-Einstein condensate by numerically solving the modified Gross-Pitaevskii equation. The testimony of such a crossover is presented via studying the fractional density of the condensate which smoothly migrates from being a flat-head curve at weak confinement to a bright soliton at strong confinement. Such a transition occurs across a region of the potential whose strength varies over an order of magnitude and thus should be fit to be termed as a crossover. We supplement our studies via exploring the size of the bound pairs and the ramifications of the particle density therein. Eventually, all of these aid us in arriving at a phase diagram in a space defined by the trap strength and the particle number that shows the formation of two phases consisting of droplets and solitons, along with a regime of coexistence of these two.Phase transitions in the Ising model on a layered triangular lattice in a magnetic fieldhttps://zbmath.org/1496.820072022-11-17T18:59:28.764376Z"Murtazaev, A. K."https://zbmath.org/authors/?q=ai:murtazaev.a-k"Badiev, M. K."https://zbmath.org/authors/?q=ai:badiev.m-k"Ramazanov, M. K."https://zbmath.org/authors/?q=ai:ramazanov.m-k"Magomedov, M. A."https://zbmath.org/authors/?q=ai:magomedov.m-aSummary: The influence of the magnetic field on phase transitions and thermodynamic properties of the Ising model on a triangular lattice was studied using the Wang-Landau algorithm and the replica algorithm of the Monte Carlo method. It is shown that in the model under study, depending on the magnitude of the magnetic field \(h\), disordered, partially ordered, and completely ordered phases are observed. The nature of phase transitions was analyzed based on the histogram method of data analysis. It was found that in the range \(0 \leq h \leq 6\) observed second-order phase transition. It was found that for values of the magnetic field \(h > 6\) there is no degeneracy of the ground state and the phase transition is destroyed. A plateau was found depending on the magnetization on the magnetic field, equal to 1/3 of the saturation magnetization.An efficient way to examine thermodynamics of relativistic ideal Fermi and Bose gaseshttps://zbmath.org/1496.820082022-11-17T18:59:28.764376Z"Çopuroğlu, Ebru"https://zbmath.org/authors/?q=ai:copuroglu.ebruSummary: The determination of thermodynamic properties such as entropy, energy, pressure, free energy and etc. is very important for all fields of thermodynamic physics. Also giving reliable analytical formulas for evaluating thermodynamic properties of relativistic ideal gases is essential. One of the way of solving thermodynamic properties of ideal Fermi and Bose Gases is determining the expression of pressure integral. In this study we have presented a new computational method for the evaluation of the pressure term of the relativistic ideal Fermi and Bose gases. The purposed method shows that obtained analytically series expansions works for any values of parameters at high temperatures.Performance of Heisenberg-coupled spins as quantum Stirling heat machine near quantum critical pointhttps://zbmath.org/1496.820092022-11-17T18:59:28.764376Z"Purkait, Chayan"https://zbmath.org/authors/?q=ai:purkait.chayan"Biswas, Asoka"https://zbmath.org/authors/?q=ai:biswas.asokaSummary: We study the performance of quantum Stirling machines based on two Heisenberg-coupled spins as the working system near quantum critical point (QCP). During the heat cycle, the spins perform either as a heat engine or a refrigerator, with changing magnetic field to the critical point. At the QCP, the efficiency of the engine and the coefficient of performance of the refrigerator attain the corresponding values of their Carnot counterparts, along with maximum work output. We analyze how such enhancement can be attributed to the nonanalytic behaviour of spin-spin correlation and the entanglement near the QCP. Further, we explore how two spins perform as a thermal machine in presence of a third spin, when all the three spins are in thermodynamic equilibrium and exhibit quantum Stirling cycle.Percolation of wormshttps://zbmath.org/1496.820102022-11-17T18:59:28.764376Z"Ráth, Balázs"https://zbmath.org/authors/?q=ai:rath.balazs"Rokob, Sándor"https://zbmath.org/authors/?q=ai:rokob.sandorSummary: We introduce a new correlated percolation model on the \(d\)-dimensional lattice \(\mathbb{Z}^d\) called the \textit{random length worms model}. Assume given a probability distribution on the set of positive integers (the length distribution) and \(v \in (0, \infty)\) (the intensity parameter). From each site of \(\mathbb{Z}^d\) we start \(\operatorname{POI} (v)\) independent simple random walks with this length distribution. We investigate the connectivity properties of the set \(\mathcal{S}^v\) of sites visited by this cloud of random walks. It is easy to show that if the second moment of the length distribution is finite then \(\mathcal{S}^v\) undergoes a percolation phase transition as \(v\) varies. Our main contribution is a sufficient condition on the length distribution which guarantees that \(\mathcal{S}^v\) percolates for all \(v > 0\) if \(d \geq 5\). E.g., if the probability mass function of the length distribution is
\[
m (\ell) = c \cdot \ln (\ln (\ell))^\varepsilon / (\ell^3 \ln (\ell)) \mathbb{1} [\ell \geq \ell_0]
\] for some \(\ell_0 > e^e\) and \(\varepsilon > 0\) then \(\mathcal{S}^v\) percolates for all \(v > 0\). Note that the second moment of this length distribution is only ``barely'' infinite. In order to put our result in the context of earlier results about similar models (e.g., finitary random interlacements, loop percolation, Bernoulli hyper-edge percolation, Poisson Boolean model, ellipses percolation, etc.), we define a natural family of percolation models called the \textit{Poisson zoo} and argue that the percolative behaviour of the random length worms model is quite close to being ``extremal'' in this family of models.A fractional Anderson modelhttps://zbmath.org/1496.820112022-11-17T18:59:28.764376Z"Molina, Mario I."https://zbmath.org/authors/?q=ai:molina.mario-iSummary: We examine the interplay between disorder and fractionality in a one-dimensional tight-binding Anderson model. In the absence of disorder, we observe that the two lowest energy eigenvalues detach themselves from the bottom of the band, as fractionality \(s\) is decreased, becoming completely degenerate at \(s = 0\), with a common energy equal to a half bandwidth, \(V\). The remaining \(N - 2\) states become completely degenerate forming a flat band with energy equal to a bandwidth, \(2V\). Thus, a gap is formed between the ground state and the band. In the presence of disorder and for a fixed disorder width, a decrease in \(s\) reduces the width of the point spectrum while for a fixed \(s\), an increase in disorder increases the width of the spectrum. For all disorder widths, the average participation ratio decreases with \(s\) showing a tendency towards localization. However, the average mean square displacement (MSD) shows a hump at low \(s\) values, signaling the presence of a population of extended states, in agreement with what is found in long-range hopping models.Emergent behaviors of discrete Lohe aggregation flowshttps://zbmath.org/1496.820122022-11-17T18:59:28.764376Z"Choi, Hyungjun"https://zbmath.org/authors/?q=ai:choi.hyungjun"Ha, Seung-Yeal"https://zbmath.org/authors/?q=ai:ha.seung-yeal"Park, Hansol"https://zbmath.org/authors/?q=ai:park.hansolSummary: The Lohe sphere model and the Lohe matrix model are prototype continuous aggregation models on the unit sphere and the unitary group, respectively. These models have been extensively investigated in recent literature. In this paper, we propose several discrete counterparts for the continuous Lohe type aggregation models and study their emergent behaviors using the Lyapunov function method. For suitable discretization of the Lohe sphere model, we employ a scheme consisting of two steps. In the first step, we solve the first-order forward Euler scheme, and in the second step, we project the intermediate state onto the unit sphere. For this discrete model, we present a sufficient framework leading to the complete state aggregation in terms of system parameters and initial data. For the discretization of the Lohe matrix model, we use the Lie group integrator method, Lie-Trotter splitting method and Strang splitting method to propose three discrete models. For these models, we also provide several analytical frameworks leading to complete state aggregation and asymptotic state-locking.Corrigendum to: ``On the reduced dynamics of a subset of interacting bosonic particles''https://zbmath.org/1496.820132022-11-17T18:59:28.764376Z"Gessner, Manuel"https://zbmath.org/authors/?q=ai:gessner.manuel"Buchleitner, Andreas"https://zbmath.org/authors/?q=ai:buchleitner.andreasCorrigendum to the authors' paper [ibid. 390, 192--213 (2018; Zbl 1384.82007)].The \(P(\phi)_2\) Euclidean quantum field theory as classical statistical mechanics. I.https://zbmath.org/1496.820142022-11-17T18:59:28.764376Z"Guerra, F."https://zbmath.org/authors/?q=ai:guerra.francesco"Rosen, L."https://zbmath.org/authors/?q=ai:rosen.lon-m"Simon, B."https://zbmath.org/authors/?q=ai:simon.barrySee the joint review of part II [the authors, ibid. 101, No. 2, 191--259 (1975; Zbl 1495.82015)].Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensatehttps://zbmath.org/1496.820152022-11-17T18:59:28.764376Z"Lampart, Jonas"https://zbmath.org/authors/?q=ai:lampart.jonas"Pickl, Peter"https://zbmath.org/authors/?q=ai:pickl.peterSummary: We consider the quantum dynamics of a large number \(N\) of interacting bosons coupled a tracer particle, i.e. a particle of another kind, on a torus. We assume that in the initial state the bosons essentially form a homogeneous Bose-Einstein condensate, with some excitations. With an appropriate mean-field scaling of the interactions, we prove that the effective dynamics for \(N\rightarrow \infty\) is generated by the Bogoliubov-Fröhlich Hamiltonian, which couples the tracer particle linearly to the excitation field.Propagation of chaos: a review of models, methods and applications. I: Models and methodshttps://zbmath.org/1496.820162022-11-17T18:59:28.764376Z"Chaintron, Louis-Pierre"https://zbmath.org/authors/?q=ai:chaintron.louis-pierre"Diez, Antoine"https://zbmath.org/authors/?q=ai:diez.antoineSummary: The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods as well as several important results in the field. The models considered include the McKean-Vlasov diffusion, the mean-field jump models and the Boltzmann models. The first part of this review is an introduction to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more detailed study of some of the important models in the field.
For Part II, see [ibid. 15, No. 6, 1017--1173 (2022; Zbl 1496.82017)].Propagation of chaos: a review of models, methods and applications. II: Applicationshttps://zbmath.org/1496.820172022-11-17T18:59:28.764376Z"Chaintron, Louis-Pierre"https://zbmath.org/authors/?q=ai:chaintron.louis-pierre"Diez, Antoine"https://zbmath.org/authors/?q=ai:diez.antoineSummary: The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods as well as several important results in the field. The models considered include the McKean-Vlasov diffusion, the mean-field jump models and the Boltzmann models. The first part of this review is an introduction to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more detailed study of some of the important models in the field.
For Part I, see [ibid. [ibid. 15, No. 6, 895--1015 (2022; Zbl 1496.82016)].Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: analytical analyses of steady state evolving from initial statehttps://zbmath.org/1496.820182022-11-17T18:59:28.764376Z"Wang, Yu-Qing"https://zbmath.org/authors/?q=ai:wang.yuqing"Wang, Chao-Fan"https://zbmath.org/authors/?q=ai:wang.chao-fan"Wang, Hao-Tian"https://zbmath.org/authors/?q=ai:wang.haotian"Du, Min-Xuan"https://zbmath.org/authors/?q=ai:du.min-xuan"Wang, Bing-Hong"https://zbmath.org/authors/?q=ai:wang.binghongSummary: Being a vital two-dimensional multibody interacting particle system in nonlinear science and complex systems, exclusion network fuses totally asymmetric simple exclusion process into underlying complex network dynamics. This study constructs equiprobable exclusion network with heterogeneous interactions by introducing randomly generated interaction rates on each random path. Nodes are equivalent to subnetworks modelled by periodic TASEPs. Analytical solutions of typical order parameters are obtained by exploring dynamical transitions among configuration probabilities validated by meticulous balance theory. Physical mechanisms of underlying exclusion network dynamics are revealed by discussing TASEP with boundaries and Langmuir kinetics. New analytical method named as isoline analyses on mechanisms of spatial correlation and spatiotemporal evolution is proposed. Phase boundaries between initial state and steady state are analytically solved, which have a high agreement with simulations. Fruitful mechanisms of system transiting from initial phase to steady phases are discovered. It will have theoretical and practical value of deeply understanding evolution laws of cluster dynamics of self-driven particles and exploring non-equilibrium phase transitions in active systems.Dynamic theory of fluctuations and critical exponents of thermodynamic phase transitionshttps://zbmath.org/1496.820192022-11-17T18:59:28.764376Z"Liu, Ruikuan"https://zbmath.org/authors/?q=ai:liu.ruikuan"Ma, Tian"https://zbmath.org/authors/?q=ai:ma.tian"Wang, Shouhong"https://zbmath.org/authors/?q=ai:wang.shouhong"Yang, Jiayan"https://zbmath.org/authors/?q=ai:yang.jiayanSummary: First we derive the dynamical law of fluctuations. Second, using the dynamic transition theory, we derive theoretical values of critical exponents from the standard model of thermodynamics with or without fluctuations. Third, we show that the standard model, together with the dynamic law of fluctuations, offers correct information for the critical exponents. Consequently we show that the critical exponents are universal, and the discrepancy between theoretical and experiment values of critical exponents is due to fluctuations.Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limithttps://zbmath.org/1496.820202022-11-17T18:59:28.764376Z"Favre, Gianluca"https://zbmath.org/authors/?q=ai:favre.gianluca"Pirner, Marlies"https://zbmath.org/authors/?q=ai:pirner.marlies"Schmeiser, Christian"https://zbmath.org/authors/?q=ai:schmeiser.christianSummary: The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of the gas and the thermal energy of the background are conserved, and the heat flow in the background is governed by the Fourier law. For the coupled nonlinear system of the kinetic and the heat equation, existence of solutions is proved on the one-dimensional torus. Spectral stability of the equilibrium is shown on the torus in arbitrary dimensions by hypocoercivity methods. The macroscopic limit towards a nonlinear cross-diffusion problem is carried out formally.A moment closure based on a projection on the boundary of the realizability domain: extension and analysishttps://zbmath.org/1496.820212022-11-17T18:59:28.764376Z"Pichard, Teddy"https://zbmath.org/authors/?q=ai:pichard.teddySummary: A closure relation for moments equations in kinetic theory was recently introduced in [the author, Kinet. Relat. Models 13, No. 6, 1243--1280 (2020; Zbl 1458.35350)], based on the study of the geometry of the set of moments. This relation was constructed from a projection of a moment vector toward the boundary of the set of moments and corresponds to approximating the underlying kinetic distribution as a sum of a chosen equilibrium distribution plus a sum of purely anisotropic Dirac distributions. The present work generalizes this construction for kinetic equations involving unbounded velocities, i.e. to the Hamburger problem, and provides a deeper analysis of the resulting moment system. Especially, we provide representation results for moment vectors along the boundary of the moment set that implies the well-definition of the model. And the resulting moment model is shown to be weakly hyperbolic with peculiar properties of hyperbolicity and entropy of two subsystems, corresponding respectively to the equilibrium and to the purely anisotropic parts of the underlying kinetic distribution.Topological invariants for interface modeshttps://zbmath.org/1496.820222022-11-17T18:59:28.764376Z"Bal, Guillaume"https://zbmath.org/authors/?q=ai:bal.guillaumeSummary: This article concerns topologically non-trivial interface Hamiltonians that find many applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected, asymmetric edge states at the interface between two two-dimensional half spaces. The asymmetric transport is characterized by a quantized interface conductivity. The objective of this article is to compute such a conductivity and show its stability under perturbations. We present two methods. The first one computes the conductivity using the winding number of branches of absolutely continuous spectrum of the interface Hamiltonian. This calculation is independent of any bulk properties but requires a sufficient understanding of the spectral decomposition of the Hamiltonian. In the fluid flow setting, it also applies in cases where the so-called bulk-interface correspondence fails. The second method establishes a bulk-interface correspondence between the interface conductivity and a so-called bulk-difference invariant. We introduce the bulk-difference invariants characterizing pairs of half spaces. We then relate the interface conductivity to the bulk-difference invariant by means of a Fedosov-Hörmander formula, which computes the index of a related Fredholm operator and is obtained using semiclassical calculus. The two methods are used to compute invariants for representative \(2 \times 2\) and \(3 \times 3\) systems of equations that appear in the applications.An application of singular traces to crystals and percolationhttps://zbmath.org/1496.820232022-11-17T18:59:28.764376Z"Azamov, N."https://zbmath.org/authors/?q=ai:azamov.nurulla-a"Hekkelman, E."https://zbmath.org/authors/?q=ai:hekkelman.e"McDonald, E."https://zbmath.org/authors/?q=ai:mcdonald.edward-a"Sukochev, F."https://zbmath.org/authors/?q=ai:sukochev.fedor-a"Zanin, D."https://zbmath.org/authors/?q=ai:zanin.dmitriy-vSummary: For a certain class of discrete metric spaces, we provide a formula for the density of states. This formula involves Dixmier traces and is proven using recent advances in operator theory. Various examples are given of metric spaces for which this formula holds, including crystals, quasicrystals and the infinite cluster resulting from super-critical bond percolation on \(\mathbb{Z}^d\).Formulation of a phonon band calculation for molecular crystals using a coarse-grained coordinate approach under periodic boundary conditionshttps://zbmath.org/1496.820242022-11-17T18:59:28.764376Z"Houjou, Hirohiko"https://zbmath.org/authors/?q=ai:houjou.hirohiko"Seshimo, Masataka"https://zbmath.org/authors/?q=ai:seshimo.masatakaSummary: A phonon band calculation scheme based on our previously proposed coarse-graining theory under periodic boundary conditions was formulated. Starting with a simple one-dimensional, one-body periodic system, we introduced the basis set of a phase-shift coordinate system that can easily afford the discrete Fourier transformation of vectors and matrices with infinite dimensions. When the unit cell contains two or more bodies, the basis set of the phase-shift coordinate system is represented with tensors. By choosing an appropriate tensor basis set of a coarse-grained space, we can approximately block-diagonalize the dynamical matrix. Then, we can obtain the inertia and stiffness matrices represented by the given coarse-grained coordinate system, upon which the application of the mass-weighted Hessian equation affords a set of angular frequencies (\(\omega\)) as functions of the wavenumber (\(k\)). Thus, the phonon band structure (\(k\)-\(\omega\) plot) is obtained based on the coarse-graining approximation. When this approximation is applied to molecular assemblies comprising hydrogen bonding, the computational error resulting from this scheme is expected to be a maximum of a few \(\mathrm{cm}^{-1}\).Nonlinear band structure of cold atoms with interaction-dependent dispersionhttps://zbmath.org/1496.820252022-11-17T18:59:28.764376Z"Guo, Ze-Hong"https://zbmath.org/authors/?q=ai:guo.ze-hong"Yu, Xue-Jia"https://zbmath.org/authors/?q=ai:yu.xue-jia"Liang, Dan-Dan"https://zbmath.org/authors/?q=ai:liang.dan-dan"Li, Guan-Qiang"https://zbmath.org/authors/?q=ai:li.guanqiang"Li, Zhi"https://zbmath.org/authors/?q=ai:li.zhi.1|li.zhiSummary: Band structure is an important tool to characterize the physical properties of periodic systems. In this work, we investigate the nonlinear spectrum and current density in cold atoms with interaction-dependent dispersion (IDD). The results reveal that IDD causes the nonlinear loop structure, which means that the dynamical stability is destroyed, resulting in the loss of superfluidity. More interestingly, the repulsive IDD induces a more complex deformation of spectrum. Different from the previous studies, the conversion between positive and negative curvature loop structures appears in the system. Furthermore, there will be a pair of triple degeneracy points on the lower band (\(n = 2n_c\)) and a double degeneracy line between them, which will uncover new physical properties, e.g., nonlinear Landau-Zener tunneling. Since the nonlinear interaction of cold atoms is highly controllable through Feshbach resonance, this fascinating phenomenon is expected to be realized in cold atomic systems in the near future.Generalising holographic superconductorshttps://zbmath.org/1496.820262022-11-17T18:59:28.764376Z"Donini, Andrea"https://zbmath.org/authors/?q=ai:donini.andrea"Enguita-Vileta, Víctor"https://zbmath.org/authors/?q=ai:enguita-vileta.victor"Esser, Fabian"https://zbmath.org/authors/?q=ai:esser.fabian"Sanz, Veronica"https://zbmath.org/authors/?q=ai:sanz.veronicaSummary: In this paper we propose a generalised holographic framework to describe superconductors. We first unify the description of \(s\)-, \(p\)-, and \(d\)-wave superconductors in a way that can be easily promoted to higher spin. Using a semianalytical procedure to compute the superconductor properties, we are able to further generalise the geometric description of the hologram beyond the AdS-Schwarzschild Black Hole paradigm and propose a set of higher-dimensional metrics which exhibit the same universal behaviour. We then apply this generalised description to study the properties of the condensate and the scaling of the critical temperature with the parameters of the higher-dimensional theory, which allows us to reproduce existing results in the literature and extend them to include a possible description of the newly observed \(f\)-wave superconducting systems.Transition pathways in cylinder-gyroid interfacehttps://zbmath.org/1496.820272022-11-17T18:59:28.764376Z"Yao, Xiaomei"https://zbmath.org/authors/?q=ai:yao.xiaomei"Xu, Jie"https://zbmath.org/authors/?q=ai:xu.jie"Zhang, Lei"https://zbmath.org/authors/?q=ai:zhang.lei.4Summary: When two distinct ordered phases contact, the interface may exhibit rich and fascinating structures. Focusing on the Cylinder-Gyroid interface system, transition pathways connecting various interface morphologies are studied armed with the Landau-Brazovskii model. Specifically, minimum energy paths are obtained by computing transition states with the saddle dynamics. We present four primary transition pathways connecting different local minima, representing four different mechanisms of the formation of the Cylinder-Gyroid interface. The connection of Cylinder and Gyroid can be either direct or indirect via Fddd with three different orientations. Under different displacements, each of the four pathways may have the lowest energy.Viscous absorption of ultra-high-frequency gravitonshttps://zbmath.org/1496.830082022-11-17T18:59:28.764376Z"Giovannini, Massimo"https://zbmath.org/authors/?q=ai:giovannini.massimoSummary: The high-frequency gravitons can be absorbed by the first and second viscosities of the post-inflationary plasma as the corresponding wavelengths reenter the Hubble radius prior to big-bang nucleosynthesis. When the total sound speed of the medium is stiffer than radiation the rate of expansion still exceeds the shear rate but the bulk viscosity is not negligible. Depending on the value of the entropy density at the end of inflation the spectral energy density of the relic gravitons gets modified in comparison with the inviscid result when the frequency ranges between the kHz band and the GHz region. In the nHz domain the spectrum inherits a known suppression due to neutrino free-streaming but also a marginal spike potentially caused by a sudden outbreak of the bulk viscosity around the quark-hadron phase transition, as suggested by the hadron spectra produced in the collisions of heavy ions.Topological confinement in Skyrme holographyhttps://zbmath.org/1496.830262022-11-17T18:59:28.764376Z"Cartwright, Casey"https://zbmath.org/authors/?q=ai:cartwright.casey"Harms, Benjamin"https://zbmath.org/authors/?q=ai:harms.benjamin-c"Kaminski, Matthias"https://zbmath.org/authors/?q=ai:kaminski.matthias"Thomale, Ronny"https://zbmath.org/authors/?q=ai:thomale.ronnyEffect of the magnetic charge on weak deflection angle and greybody bound of the black hole in Einstein-Gauss-Bonnet gravityhttps://zbmath.org/1496.830292022-11-17T18:59:28.764376Z"Javed, Wajiha"https://zbmath.org/authors/?q=ai:javed.wajiha"Aqib, Muhammad"https://zbmath.org/authors/?q=ai:aqib.muhammad"Övgün, Ali"https://zbmath.org/authors/?q=ai:ovgun.aliSummary: The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.On superstatistics and black hole quasinormal modeshttps://zbmath.org/1496.830302022-11-17T18:59:28.764376Z"Martínez-Merino, A."https://zbmath.org/authors/?q=ai:martinez-merino.aldo-a"Sabido, M."https://zbmath.org/authors/?q=ai:sabido.miguelSummary: It is known that using Boltzmann-Gibbs statistics, Bekenstein-Hawking entropy \(S_{HB}\), and the quasinormal modes of black holes, one finds that the lowest value of spin is \(j_{min} = 1\). In this paper, we determine \(j_{min}\), using non-extensive entropies that depend only on the probability (known as Obregon's entropies and have been derived from superstatistics). We also calculate \(j_{min}\) for a set of non-extensive entropies that have free parameters and are written in terms of \(S_{BH}\). We find that \(j_{min}\) depends on the area and the non-extensive parameter.
For the non-extensive entropies that only depend on the probability, we find that the modification is only present for micro black holes. For classical black holes the results are the same as for the Boltzmann-Gibbs statistics.Uniformly accelerated Brownian oscillator in (2+1)D: temperature-dependent dissipation and frequency shifthttps://zbmath.org/1496.830352022-11-17T18:59:28.764376Z"Moustos, Dimitris"https://zbmath.org/authors/?q=ai:moustos.dimitrisSummary: We consider an Unruh-DeWitt detector modeled as a harmonic oscillator that is coupled to a massless quantum scalar field in the (2+1)-dimensional Minkowski spacetime. We treat the detector as an open quantum system and employ a quantum Langevin equation to describe its time evolution, with the field, which is characterized by a frequency-independent spectral density, acting as a stochastic force. We investigate a point-like detector moving with constant acceleration through the Minkowski vacuum and an inertial one immersed in a thermal reservoir at the Unruh temperature, exploring the implications of the well-known non-equivalence between the two cases on their dynamics. We find that both the accelerated detector's dissipation rate and the shift of its frequency caused by the coupling to the field bath depend on the acceleration temperature. Interestingly enough this is not only in contrast to the case of inertial motion in a heat bath but also to any analogous quantum Brownian motion model in open systems, where dissipation and frequency shifts are not known to exhibit temperature dependencies. Nonetheless, we show that the fluctuating-dissipation theorem still holds for the detector-field system and in the weak-coupling limit an accelerated detector is driven at late times to a thermal equilibrium state at the Unruh temperature.Interaction of inhomogeneous axions with magnetic fields in the early universehttps://zbmath.org/1496.830382022-11-17T18:59:28.764376Z"Dvornikov, Maxim"https://zbmath.org/authors/?q=ai:dvornikov.maximSummary: We study the system of interacting axions and magnetic fields in the early universe after the quantum chromodynamics phase transition, when axions acquire masses. Both axions and magnetic fields are supposed to be spatially inhomogeneous. We derive the equations for the spatial spectra of these fields, which depend on conformal time. In case of the magnetic field, we deal with the spectra of the energy density and the magnetic helicity density. The evolution equations are obtained in the closed form within the mean field approximation. We choose the parameters of the system and the initial condition which correspond to realistic primordial magnetic fields and axions. The system of equations for the spectra is solved numerically. We compare the cases of inhomogeneous and homogeneous axions. The evolution of the magnetic field in these cases is different only within small time intervals. Generally, magnetic fields are driven mainly by the magnetic diffusion. We find that the magnetic field instability takes place for the amplified initial wavefunction of the homogeneous axion. This instability is suppressed if we account for the inhomogeneity of the axion.Quark condensate and chiral symmetry restoration in neutron starshttps://zbmath.org/1496.850012022-11-17T18:59:28.764376Z"Jin, Hao-Miao"https://zbmath.org/authors/?q=ai:jin.hao-miao"Xia, Cheng-Jun"https://zbmath.org/authors/?q=ai:xia.cheng-jun"Sun, Ting-Ting"https://zbmath.org/authors/?q=ai:sun.tingting"Peng, Guang-Xiong"https://zbmath.org/authors/?q=ai:peng.guang-xiongSummary: Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of \(\rho^3\), we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of reach for neutron stars.Structure of magnetized strange quark star in perturbative QCDhttps://zbmath.org/1496.850042022-11-17T18:59:28.764376Z"Sedaghat, J."https://zbmath.org/authors/?q=ai:sedaghat.j"Zebarjad, S. M."https://zbmath.org/authors/?q=ai:zebarjad.s-mohammad|zebarjad.seyed-mostafa"Bordbar, G. H."https://zbmath.org/authors/?q=ai:bordbar.g-h"Eslam Panah, B."https://zbmath.org/authors/?q=ai:eslam-panah.bSummary: We have performed the leading order perturbative calculation to obtain the equation of state (EoS) of the strange quark matter (SQM) at zero temperature under the magnetic field \(B = 10^{18}G\). The SQM comprises two massless quark flavors (up and down) and one massive quark flavor (strange). Consequently, we have used the obtained EoS to calculate the maximum gravitational mass and the corresponding radius of the magnetized strange quark star (SQS). We have employed two approaches, including the regular perturbation theory (\textbf{RPT}) and the background perturbation theory (\textbf{BPT}). In \textbf{RPT} the infrared (IR) freezing effect of the coupling constant has not been accounted for, while this effect has been included in \textbf{BPT}. We have obtained the value of the maximum gravitational mass to be more than three times the solar mass. The validity of isotropic structure calculations for SQS has also been investigated. Our results show that the threshold magnetic field from which an anisotropic approach begins to be significant lies in the interval \(2 \times 10^{18}G < B < 3 \times 10^{18}G\). Furthermore, we have computed the redshift, compactness and Buchdahl-Bondi bound of the SQS to show that this compact object cannot be a black hole.Group chase and escape. Fusion of pursuits-escapes and collective motionshttps://zbmath.org/1496.920022022-11-17T18:59:28.764376Z"Kamimura, Atsushi"https://zbmath.org/authors/?q=ai:kamimura.atsushi"Ohira, Toru"https://zbmath.org/authors/?q=ai:ohira.toruThe book under review is a result of collaboration of researchers with the experience in two different areas of mathematics. The interest of the first author in the development of theoretical models explaining consistent growth and division of primitive cells and the work of the second author with the models of a random walk with delay led to the publication of the book combining classical mathematical problems of chases and escapes with an emerging research field studying collective motions of ``self-driven'' particles.
In the introductory Chapter 1, the origins of the two fields, chases and escapes and collective motions, are discussed. Both have a long and interesting history. The formulation of the first chase and escape problem is attributed to Leonardo da Vinci who considered a cat-chasing-a-mouse problem and the first studies of multi-particle systems in physics are related to the work of Johannes Kepler who investigated relations between the geometry and motion of six planets based on the astronomical data collected by Tycho Brahe. The authors argue that a model of a ``group chase and escape'' can be viewed either as a ``simple extension of the traditional chase and escape problems to multiple players'' or as an ``extension of the self-propelled particles into a mixture of two groups with different motives''. Some of the recent research developments are briefly described along with potential applications of group chases and escapes and open problems.
Chapter 2 introduces the reader to representative problems including chases and escapes along straight lines and along circular paths in the plane. The extensions to 3D space allowing targets to move along circular cylindrical helices and equiangular spiral helices are also considered.
Fundamental concepts of statistical mechanics (phase transition, order parameters, symmetry, critical exponents, spin models) are discussed in Chapter 3. These are used to explain phase transition in equilibrium models and collective motion in non-equilibrium models. Two theoretical models are analysed, the Vicsek flocking model and the optimal velocity model. The latter one describes traffic jams on highways in a 1D case whereas its 2D extension models collective motion of pedestrians and animals.
Chapter 4 is fundamental for the understanding of a concept of group chase and escape which fuses two research fields introduced in Chapters 2 and 3. The basic model is built on the following simple rule: a chaser tries to get closer to the nearest target and a target attempts to get away from the nearest chaser. The lifetimes of targets are calculated and their dependence on the number of chasers and initial targets are explored. For the quantitative analysis of chasing processes, a simple classification focusing on ``one-particle-to-many-opponents situations'' is considered. In the final part of the chapter, recent developments in group chases and escapes are discussed from the view points of abilities (modifications of the model allowing agents to detect the opponents' positions), reactions (modifications of the model reflecting how the targets that are captured affect their species and mortality), and motions (modifications of the rules restricting spatial motion of particles).
The final Chapter 5 addresses a number of open problems in group chases and escapes and provides possible directions for future developments in the field. The crucial role of boundary conditions is first discussed; the authors argue that the choice of an appropriate kind of boundary condition is highly nontrivial; it depends on the aspects of the system one wants to study and impacts the understanding of the general behavior of group chase and escape. Challenging issues regarding the characterisation and distribution of chasing patterns and their dependence on the initial conditions are also addressed. Two representative examples for flocking and traffic flow are considered to illustrate the development of macroscopic models which describe collective behavior. Potential applications of group chases and escapes considered in this chapter include hunting in nature, optimisation problems, and a sketch of a ``general perspective on the power of living together.'' There are four appendices in the book illustrating interesting variations and extensions of chases and escapes: Discrete search game on graphs, Chase and escape with delays, Virtual stick balancing, and minority games. The rich list of references includes 105 items.
The book is well-written, explanations are concise and transparent, and the excellent quality of the print with many illustrations in color matches the quality of the exposition. It is an interesting introduction to a new area of research bridging pursuits-escapes with collective motions where, according to the authors, ''the successful fusion of the two topics remains to be achieved.''
Reviewer: Svitlana P. Rogovchenko (Kristiansand)