Recent zbMATH articles in MSC 82https://zbmath.org/atom/cc/822023-11-13T18:48:18.785376ZUnknown authorWerkzeugMini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 -- December 3, 2022https://zbmath.org/1521.000202023-11-13T18:48:18.785376ZSummary: In many situations, most prominently in quantum mechanics, it is important to understand well the eigenvalues and associated eigenfunctions of certain self-adjoint differential operators. The goal of this workshop was to study the strong link between spectral properties of such operators and the underlying geometry which might be randomly generated. By combining ideas and methods from spectral geometry and probability theory, we hope to stimulate new research including important topics such as Bose-Einstein condensation in random environments.Gaudin algebras, RSK and Calogero-Moser cells in type Ahttps://zbmath.org/1521.052122023-11-13T18:48:18.785376Z"Brochier, Adrien"https://zbmath.org/authors/?q=ai:brochier.adrien"Gordon, Iain"https://zbmath.org/authors/?q=ai:gordon.iain-g"White, Noah"https://zbmath.org/authors/?q=ai:white.noahSummary: We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the \(n\)-fold tensor representation \({\mathbb{C}}[x_1, \ldots , x_r]^{\otimes n}\) of the Lie algebra \(\mathfrak{gl}_r\). We use the work of \textit{I. Halacheva} et al. [Duke Math. J. 169, No. 12, 2337--2419 (2020; Zbl 1468.17013)] to demonstrate that the Robinson-Schensted-Knuth correspondence describes the behaviour of the spectrum as we move along special paths in the family. We apply the work of \textit{E. Mukhin} et al. [SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 072, 11 p. (2012; Zbl 1269.82018); St. Petersbg. Math. J. 22, No. 3, 463--472 (2011; Zbl 1219.82121); translation from Algebra Anal. 2010, No. 3, 177--190 (2010)], which proves that the rational Calogero-Moser phase space can be realised as a part of this spectrum, to relate this to behaviour at \(t=0\) of rational Cherednik algebras of \(\mathfrak{S}_n\). As a result, we confirm for symmetric groups a conjecture of \textit{C. Bonnafé} and \textit{R. Rouquier} [``Cherednik algebras and Calogero-Moser cells'', Preprint, \url{arXiv:1708.09764}] which proposes an equality between the Calogero-Moser cells they defined and the well-known Kazhdan-Lusztig cells.
{{\copyright} 2023 The Authors. \textit{Proceedings of the London Mathematical Society} is copyright {\copyright} London Mathematical Society.}Hyperbolic limit for a biological invasionhttps://zbmath.org/1521.350132023-11-13T18:48:18.785376Z"Hilhorst, Danielle"https://zbmath.org/authors/?q=ai:hilhorst.danielle"Kim, Yongjung"https://zbmath.org/authors/?q=ai:kim.yongjung"Nguyen, Thanh Nam"https://zbmath.org/authors/?q=ai:nguyen.thanh-nam"Park, Hyunjoon"https://zbmath.org/authors/?q=ai:park.hyunjoonSummary: In a spatially heterogeneous environment the propagation speed of a biological invasion varies in space. The traveling wave theory in a homogeneous case is not extended to a heterogeneous case. Taking a singular limit in a hyperbolic scale is a good way to study such a wave propagation with constant speed. The goal of this project is to understand the effect of biological diffusion on the wave speed in a spatial heterogeneous environment. For this purpose, we consider \[U_t=\varepsilon(\gamma(s)U)_{xx}+\frac{1}{\varepsilon}U(1-U/m(x)),\] where \(m\) is a nonconstant carrying capacity, \(s=\frac{U}{m}\) is a starvation measure and \(\gamma(s)=s^{\tilde{k}}\), \(\widetilde{k}\ge 1\). The diffusion is a starvation driven diffusion. We show that the diffusion speed is constant even if \(m\) is nonconstant.Large-scale asymptotics of velocity-jump processes and nonlocal Hamilton-Jacobi equationshttps://zbmath.org/1521.350822023-11-13T18:48:18.785376Z"Bouin, Emeric"https://zbmath.org/authors/?q=ai:bouin.emeric"Calvez, Vincent"https://zbmath.org/authors/?q=ai:calvez.vincent"Grenier, Emmanuel"https://zbmath.org/authors/?q=ai:grenier.emmanuel"Nadin, Grégoire"https://zbmath.org/authors/?q=ai:nadin.gregoireSummary: We investigate a simple velocity jump process in the regime of large deviation asymptotics. New velocities are taken randomly at a constant, large, rate from a Gaussian distribution with vanishing variance. The Kolmogorov forward equation associated with this process is the linear BGK kinetic transport equation. We derive a new type of Hamilton-Jacobi equation which is nonlocal with respect to the velocity variable. We introduce a suitable notion of viscosity solution, and we prove well-posedness in the viscosity sense. We also prove convergence of the logarithmic transformation toward this limit problem. Furthermore, we identify the variational formulation of the solution by means of an action functional supported on piecewise linear curves. As an application of this theory, we compute the exact rate of acceleration in a kinetic version of the celebrated F-KPP equation in the one-dimensional case.Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary conditionhttps://zbmath.org/1521.351322023-11-13T18:48:18.785376Z"Bernou, Armand"https://zbmath.org/authors/?q=ai:bernou.armand"Carrapatoso, Kleber"https://zbmath.org/authors/?q=ai:carrapatoso.kleber"Mischler, Stéphane"https://zbmath.org/authors/?q=ai:mischler.stephane"Tristani, Isabelle"https://zbmath.org/authors/?q=ai:tristani.isabelleThe subject of this work consists of the consideration of kinetic equations describing a variation of the density function corresponding to particles moving within a sufficiently smooth boundary in such a way that either the Boltzmann or the Landau collision operator is applicable. The specific feature of the considered problem is the position-dependent Maxwell boundary conditions varying from the pure specular reflection to the pure diffusive boundary condition and allowing the consideration of a weakly non-equilibrium system interacting with the equilibrated thermostat. The main result consists of establishing the convergence to the equilibrium in such a general situation in a uniform way including the transition to the hydrodynamic limit.
Reviewer: Eugene Postnikov (Kursk)Asymptotic stability of a nonlinear wave for an outflow problem of the bipolar Navier-Stokes-Poisson system under large initial perturbationhttps://zbmath.org/1521.351432023-11-13T18:48:18.785376Z"Wu, Qiwei"https://zbmath.org/authors/?q=ai:wu.qiwei"Hou, Xiaofeng"https://zbmath.org/authors/?q=ai:hou.xiaofeng"Zhu, Peicheng"https://zbmath.org/authors/?q=ai:zhu.peichengSummary: In this paper, we study the time-asymptotic behavior of solutions to an outflow problem for the one-dimensional bipolar Navier-Stokes-Poisson system in the half space. First, we make some suitable assumptions on the boundary data and space-asymptotic states such that the time-asymptotic state of the solution is a nonlinear wave, which is the superposition of the transonic stationary solution and the 2-rarefaction wave. Next, we show the stability of this nonlinear wave under a class of large initial perturbation, provided that the strength of the transonic stationary solution is small enough, while the amplitude of the 2-rarefaction wave can be arbitrarily large. The proof is completed by a delicate energy method and a continuation argument. The key point is to derive the positive upper and lower bounds of the particle densities.A complete proof that square ice entropy is \(\frac{3}{2}\log_2(4/3)\)https://zbmath.org/1521.370062023-11-13T18:48:18.785376Z"Gangloff, Silvère"https://zbmath.org/authors/?q=ai:gangloff.silvereThe author provides many details for the beautiful formula of the square ice entropy found by \textit{E. Lieb} [Phys. Rev. 162, No. 1, 162--172 (1967; \url{doi:10.1103/PhysRev.162.162})]. More specifically, consider a graph with \(\mathbb{Z}^2\) as vertices, and let the edges be obtained by connecting nearest neighbor vertices. Restrict this graph to lie within the closed box \([1,N]^2\) for large integer \(N\). A configuration is an assignment of arrows to each edge so that at each vertex, two arrows come in and go out from that vertex. Impose periodic boundary conditions. Then the formula for the square ice entropy is:
\[
\lim_{N\to+\infty}\frac{\log_2(\text{Number of configurations within } [1,N^2])}{N^2}=\frac32\cdot\log_2\left(\frac43\right)
\]
A brief outline for the proof to establish this formula follows. One of the first tasks is to relate the large \(N\) behavior of the number of configurations within \([1,N]^2\) to the largest eigenvalue of the \(2N\times2N\) transfer matrix \(V_N(1)\). It turns out that there is a candidate formula for the eigenvalues and the eigenvectors for the transfer matrix \(V_N(1)\) due to \textit{H. Bethe} [Z. Phys. 71, 205--226 (1931; Zbl 0002.37205)]. The author shows that if the set of the Bethe equations can be solved, then the candidate eigenvalues and the eigenvectors are indeed eigenvalues and eigenvectors for the transfer matrix \(V_N(1)\). The next task is to show that one of the candidate eigenvalue is the largest eigenvalue for the transfer matrix \(V_N(1)\). In the large \(N\) limit, the Bethe equations lead to a Fredholm integral equation that can be explicitly solved. With an explicit solution for the Fredholm integral equation, the largest eigenvalue can be expressed in terms of an integral over an interval on the real number line with an explicit integrand in the large \(N\) limit. This integral can be evaluated exactly with the complex analysis residue theorem. Thus, Lieb's square ice entropy formula is obtained.
Reviewer: Haru Pinson (Tucson)Some breathers and multi-breathers for FPU-type chainshttps://zbmath.org/1521.370872023-11-13T18:48:18.785376Z"Arioli, Gianni"https://zbmath.org/authors/?q=ai:arioli.gianni"Koch, Hans"https://zbmath.org/authors/?q=ai:koch.hans-friedrichSummary: We consider several breather solutions for FPU-type chains that have been found numerically. Using computer-assisted techniques, we prove that there exist true solutions nearby, and in some cases, we determine whether or not the solution is spectrally stable. Symmetry properties are considered as well. In addition, we construct solutions that are close to (possibly infinite) sums of breather solutions.Ergodicity and long-time behavior of the random batch method for interacting particle systemshttps://zbmath.org/1521.370972023-11-13T18:48:18.785376Z"Jin, Shi"https://zbmath.org/authors/?q=ai:jin.shi"Li, Lei"https://zbmath.org/authors/?q=ai:li.lei.1"Ye, Xuda"https://zbmath.org/authors/?q=ai:ye.xuda"Zhou, Zhennan"https://zbmath.org/authors/?q=ai:zhou.zhennanSummary: We study the geometric ergodicity and the long-time behavior of the Random Batch Method for interacting particle systems, which exhibits superior numerical performance in recent large-scale scientific computing experiments. We show that for both the interacting particle system (IPS) and the random batch interacting particle system (RB-IPS), the distribution laws converge to their respective invariant distributions exponentially, and the convergence rate does not depend on the number of particles \(N\), the time step \(\tau\) for batch divisions or the batch size \(p\). Moreover, the Wasserstein-1 distance between the invariant distributions of the IPS and the RB-IPS is bounded by \(O(\sqrt{\tau})\), showing that the RB-IPS can be used to sample the invariant distribution of the IPS accurately with greatly reduced computational cost.Injective tensor products in strict deformation quantizationhttps://zbmath.org/1521.460322023-11-13T18:48:18.785376Z"Murro, Simone"https://zbmath.org/authors/?q=ai:murro.simone"van de Ven, Christiaan J. F."https://zbmath.org/authors/?q=ai:van-de-ven.christiaan-j-fSummary: The aim of this paper is twofold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly we discuss the existence of products of KMS states. As an application, we discuss the correspondence between quantum and classical Hamiltonians in spin systems and we provide a relation between the resolvent of Schödinger operators for non-interacting many particle systems and quantization maps.Mixing of the averaging process and its discrete dual on finite-dimensional geometrieshttps://zbmath.org/1521.600182023-11-13T18:48:18.785376Z"Quattropani, Matteo"https://zbmath.org/authors/?q=ai:quattropani.matteo"Sau, Federico"https://zbmath.org/authors/?q=ai:sau.federicoThe averaging process is a Markovian model of mass redistribution among nearest-neighboring sites of a graph and closely related to a large number of other models. In this paper a generalization of \(L^1\)-mixing of the averaging process and its discrete dual on finite dimensional geometries is given. The setting is that of large undirected graphs satisfying finite-dimensional Nash inequalities. A complete picture of the total variation mixing of a discrete dual of the averaging process, which here is called binomial splitting process, is obtained. A spectral gap identity for the binomial splitting process is obtained, showing that the \(k\)-particle system's spectral gap coincides with the spectral gap of the single-particle system on any graph. Multicolored averaging are introduced and a intertwining relation with binomial splitting process is proved. Sharp upper bounds for the averaging process from proprieties of a few-particle binomial splitting are derived and results on the many-particle binomial splitting are deduced.
Reviewer: Ilie Valuşescu (Bucureşti)Some properties of the Runge-Kutta-Legendre super-time-stepping explicit methodshttps://zbmath.org/1521.650632023-11-13T18:48:18.785376Z"Dawes, A. S."https://zbmath.org/authors/?q=ai:dawes.alan-sSummary: In this paper we will show that the Runge-Kutta-Legendre (RKL) super-time-step methods are built up in stages by combining forward Euler steps with linear extrapolation steps. For second order, we will show that linear interpolation is also used. By using these characteristics a simplified algorithm will be presented. The effect of different types of external boundary conditions are shown. For Neumann (zero-flux) and Periodic the methods are shown to be monotone. For Dirichlet it is shown that there are regions of non-monotonicity where solutions have the potential to go negative. These solutions are nonphysical and will lead to erroneous results if they are feed back into system. To remove these limitations two solution strategies are presented based on different non-uniform fixed meshing philosophies. A number of applications are shown with solutions validated against analytic. For a monotone heat front and a diffused heat pulse, the RKL results are shown to be physically correct and computationally cheaper. For a compact heat pulse it will be shown that adverse effects can occur if the number of steps is too large. It will be shown that results are significantly improved by reducing the number of steps and increasing the number of outer cycles. For general applications the universal approach is to try different numbers of steps and then study any sensitivities.Neural networks and deep learning. A textbookhttps://zbmath.org/1521.680012023-11-13T18:48:18.785376Z"Aggarwal, Charu C."https://zbmath.org/authors/?q=ai:aggarwal.charu-cPublisher's description: This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of deep learning. The theory and algorithms of neural networks are particularly important for understanding important concepts, so that one can understand the important design concepts of neural architectures in different applications. Why do neural networks work? When do they work better than off-the-shelf machine-learning models? When is depth useful? Why is training neural networks so hard? What are the pitfalls? The book is also rich in discussing different applications in order to give the practitioner a flavor of how neural architectures are designed for different types of problems. Deep learning methods for various data domains, such as text, images, and graphs are presented in detail. The chapters of this book span three categories:
The basics of neural networks: The backpropagation algorithm is discussed in Chapter 2.
Many traditional machine learning models can be understood as special cases of neural networks. Chapter 3 explores the connections between traditional machine learning and neural networks. Support vector machines, linear/logistic regression, singular value decomposition, matrix factorization, and recommender systems are shown to be special cases of neural networks.
Fundamentals of neural networks: A detailed discussion of training and regularization is provided in Chapters 4 and 5. Chapters 6 and 7 present radial-basis function (RBF) networks and restricted Boltzmann machines.
Advanced topics in neural networks: Chapters 8, 9, and 10 discuss recurrent neural networks, convolutional neural networks, and graph neural networks. Several advanced topics like deep reinforcement learning, attention mechanisms, transformer networks, Kohonen self-organizing maps, and generative adversarial networks are introduced in Chapters 11 and 12.
The textbook is written for graduate students and upper under graduate level students. Researchers and practitioners working within this related field will want to purchase this as well.
Where possible, an application-centric view is highlighted in order to provide an understanding of the practical uses of each class of techniques.The second edition is substantially reorganized and expanded with separate chapters on backpropagation and graph neural networks. Many chapters have been significantly revised over the first edition.
Greater focus is placed on modern deep learning ideas such as attention mechanisms, transformers, and pre-trained language models.
See the review of the first edition in [Zbl 1402.68001].On the effective initialisation for restricted Boltzmann machines via duality with Hopfield modelhttps://zbmath.org/1521.681332023-11-13T18:48:18.785376Z"Leonelli, Francesca Elisa"https://zbmath.org/authors/?q=ai:leonelli.francesca-elisa"Agliari, Elena"https://zbmath.org/authors/?q=ai:agliari.elena"Albanese, Linda"https://zbmath.org/authors/?q=ai:albanese.linda"Barra, Adriano"https://zbmath.org/authors/?q=ai:barra.adrianoSummary: Restricted Boltzmann machines (RBMs) with a binary visible layer of size \(N\) and a Gaussian hidden layer of size \(P\) have been proved to be equivalent to a Hopfield neural network (HNN) made of \(N\) binary neurons and storing \(P\) patterns \(\boldsymbol{\xi}\), as long as the weights \(\boldsymbol{w}\) in the former are identified with the patterns. Here we aim to leverage this equivalence to find effective initialisations for weights in the RBM when what is available is a set of noisy examples of each pattern, aiming to translate statistical mechanics background available for HNN to the study of RBM's learning and retrieval abilities. In particular, given a set of definite, structureless patterns we build a sample of blurred examples and prove that the initialisation where \(\boldsymbol{w}\) corresponds to the empirical average \(\overline{\boldsymbol{\xi}}\) over the sample is a fixed point under stochastic gradient descent. Further, as a toy application of the duality between HNN and RBM, we consider the simplest random auto-encoder (a three layer network made of two RBMs coupled by their hidden layer) and evidence that, as long as the parameter setting corresponds to the retrieval region of the dual HNN, reconstruction and denoising can be accomplished trivially, while when the system is in the spin-glass phase inference algorithms are necessary. This questions the need for larger retrieval regions which we obtain by applying a Gram-Schmidt orthogonalisation to the patterns: in fact, this procedure yields to a set of patterns devoid of correlations and for which the largest retrieval region can be accomplished. Finally we consider an application of duality also in a structured case: we test this approach on the MNIST dataset, and obtain that the network performs already \(\sim 67\%\) of successful classifications, suggesting it can be exploited as a computationally-cheap pre-training.Robustifying models against adversarial attacks by Langevin dynamicshttps://zbmath.org/1521.682012023-11-13T18:48:18.785376Z"Srinivasan, Vignesh"https://zbmath.org/authors/?q=ai:srinivasan.vignesh"Rohrer, Csaba"https://zbmath.org/authors/?q=ai:rohrer.csaba"Marban, Arturo"https://zbmath.org/authors/?q=ai:marban.arturo"Müller, Klaus-Robert"https://zbmath.org/authors/?q=ai:muller.klaus-robert"Samek, Wojciech"https://zbmath.org/authors/?q=ai:samek.wojciech"Nakajima, Shinichi"https://zbmath.org/authors/?q=ai:nakajima.shinichiSummary: Adversarial attacks on deep learning models have compromised their performance considerably. As remedies, a number of defense methods were proposed, which however, have been circumvented by newer and more sophisticated attacking strategies. In the midst of this ensuing arms race, the problem of robustness against adversarial attacks still remains a challenging task. This paper proposes a novel, simple yet effective defense strategy where off-manifold adversarial samples are driven towards high density regions of the data generating distribution of the (unknown) target class by the Metropolis-adjusted Langevin algorithm (MALA) with \textit{perceptual boundary taken into account}. To achieve this task, we introduce a \textit{generative} model of the conditional distribution of the inputs given labels that can be learned through a supervised Denoising Autoencoder (sDAE) in alignment with a \textit{discriminative} classifier. Our algorithm, called MALA for DEfense (MALADE), is equipped with significant dispersion-projection is distributed broadly. This prevents white box attacks from accurately aligning the input to create an adversarial sample effectively. MALADE is applicable to any existing classifier, providing robust defense as well as off-manifold sample detection. In our experiments, MALADE exhibited state-of-the-art performance against various elaborate attacking strategies.External forces in the continuum limit of discrete systems with non-convex interaction potentials: compactness for a \(\Gamma \)-developmenthttps://zbmath.org/1521.740072023-11-13T18:48:18.785376Z"Carioni, Marcello"https://zbmath.org/authors/?q=ai:carioni.marcello"Fischer, Julian"https://zbmath.org/authors/?q=ai:fischer.julian"Schlömerkemper, Anja"https://zbmath.org/authors/?q=ai:schlomerkemper.anjaSummary: This paper is concerned with equilibrium configurations of one-dimensional particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness results for a \(\Gamma \)-development of the energy with the novelty that external forces are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates and thus may model dead as well as live loads. Our result is based on a new technique for deriving compactness results which are required for calculating the first-order \(\Gamma \)-limit in the presence of external forces: instead of comparing a configuration of \(n\) atoms to a global minimizer of the \(\Gamma \)-limit, we compare the configuration to a minimizer in some subclass of functions which in some sense are ``close to'' the configuration. The paper is complemented with the study of the minimizers of the \(\Gamma \)-limit.Spatial vibrations and instability of axially loaded-torqued beam-like nanostructures via surface elasticity theoryhttps://zbmath.org/1521.740952023-11-13T18:48:18.785376Z"Li, Min"https://zbmath.org/authors/?q=ai:li.min.25"Wang, Chenxia"https://zbmath.org/authors/?q=ai:wang.chenxia"Kiani, Keivan"https://zbmath.org/authors/?q=ai:kiani.keivan(no abstract)Natural frequency investigation of graphene oxide powder nanocomposite cylindrical shells surrounded by Winkler/Pasternak/Kerr elastic foundations with a focus on various boundary conditionshttps://zbmath.org/1521.741422023-11-13T18:48:18.785376Z"Sobhani, Emad"https://zbmath.org/authors/?q=ai:sobhani.emad"Koohestani, Mehdi"https://zbmath.org/authors/?q=ai:koohestani.mehdi"Civalek, Ömer"https://zbmath.org/authors/?q=ai:civalek.omer"Avcar, Mehmet"https://zbmath.org/authors/?q=ai:avcar.mehmet(no abstract)Energy law preserving continuous finite element schemes for a gas metal arc welding systemhttps://zbmath.org/1521.742272023-11-13T18:48:18.785376Z"Lin, Yanhai"https://zbmath.org/authors/?q=ai:lin.yanhai"Jiang, Yongyue"https://zbmath.org/authors/?q=ai:jiang.yongyueSummary: In this paper a modified continuous energy law was explored to investigate transport behavior in a gas metal arc welding (GMAW) system. The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme. The mass conservation and current density continuous equation with the penalty scheme was applied to improve the stability. According to the phase-field model coupled with the energy law preserving method, the GMAW model was discretized and a metal transfer process with a pulse current was simulated. It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography. Compared with the numerical solution of the volume of fluid model, which was widely studied in the GMAW system based on the finite element method Euler scheme, the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.Boundary element modeling of fractional nonlinear generalized photothermal stress wave propagation problems in FG anisotropic smart semiconductorshttps://zbmath.org/1521.743172023-11-13T18:48:18.785376Z"Fahmy, Mohamed Abdelsabour"https://zbmath.org/authors/?q=ai:fahmy.mohamed-abdelsabourSummary: The main aim of this article is to develop an efficient boundary element method (BEM) modeling of the fractional nonlinear generalized photo thermal stress wave propagation problems in the context of functionally graded (FG) anisotropic smart semiconductors. Due to nonlinearity, fractional order heat conduction and strongly anisotropy of mechanical properties, the governing equations system of such problems is often very difficult to solve using classical analytical methods. Therefore, a reliable and efficient coupling scheme based on BEM was proposed to address this challenge, where, the Cartesian transformation method (CTM) has been implemented to calculate the domain integrals, and the generalized modified shift-splitting (GMSS) has been implemented for solving the linear systems arising from BEM. The calculation findings are depicted in graphical forms to display the impacts of temperature-dependent, anisotropy, piezoelectric, graded parameter and fractional parameter on the nonlinear photo thermal stress wave propagation in the considered structure. The numerical findings confirm the consistency and efficacy of the developed modeling methodology.Analysis of a penny-shaped crack with semi-permeable boundary conditions across crack face in a 3D thermal piezoelectric semiconductorhttps://zbmath.org/1521.743692023-11-13T18:48:18.785376Z"Yang, ChangHai"https://zbmath.org/authors/?q=ai:yang.changhai"Zhao, MingHao"https://zbmath.org/authors/?q=ai:zhao.minghao"Lu, Chunsheng"https://zbmath.org/authors/?q=ai:lu.chunsheng"Zhang, QiaoYun"https://zbmath.org/authors/?q=ai:zhang.qiaoyunSummary: In this paper, we study a penny-shaped crack model with electrically and thermally semi-permeable boundary conditions in a three-dimensional transversely isotropic piezoelectric semiconductor. An extended displacement discontinuity boundary element method together with an iterative process is proposed to analyze the penny-shaped crack model. The extended displacement discontinuities across crack face, electric displacement and heat flux along an inner crack cavity, as well as extended stress intensity factors near crack front are obtained via the proposed method. The effects on extended intensity factors near crack front are discussed, including boundary conditions across crack face, applied loads and initial electron concentration. It is shown that boundary conditions across crack face significantly affect extended stress intensity factors near crack front. This implies that a larger initial electron concentration can lead to electrical failure.Composite operators of stochastic model Ahttps://zbmath.org/1521.761622023-11-13T18:48:18.785376Z"Davletbaeva, D."https://zbmath.org/authors/?q=ai:davletbaeva.d"Hnatič, M."https://zbmath.org/authors/?q=ai:hnatich.michal"Komarova, M. V."https://zbmath.org/authors/?q=ai:komarova.m-v"Lučivjanský, T."https://zbmath.org/authors/?q=ai:lucivjansky.tomas"Mižišin, L."https://zbmath.org/authors/?q=ai:mizisin.lukas"Nalimov, M. Yu."https://zbmath.org/authors/?q=ai:nalimov.mikhail-yurevichSummary: By means of the field-theoretic renormalization group, we study the damping of the viscosity coefficient near the superfluid phase transition. We use the fact that in the infrared region, the complex model used to describe the phase transition belongs to the same universality class as the well-known stochastic model A. This allows us to determine the critical behavior of viscosity using composite operators for model A. Our analysis is based on the \(\varepsilon \)-expansion near the upper critical dimension \(d_{\text c} =4\) of model A. The critical exponent of viscosity is then calculated from the critical dimensions of composite operators of massless two-component model A. In particular, we present results for critical dimensions of a selected class of composite operators with the canonical dimension 8 to the leading order.Numerical study of two-phase turbulence nanofluid flow in a circular heatsink for cooling LEDs by changing their location and dimensionshttps://zbmath.org/1521.761802023-11-13T18:48:18.785376Z"Mustafa, Jawed"https://zbmath.org/authors/?q=ai:mustafa.jawed"Abdullah, M. M."https://zbmath.org/authors/?q=ai:abdullah.m-m"Ahmad, Mohammad Zaki"https://zbmath.org/authors/?q=ai:ahmad.mohammad-zaki"Husain, Shahid"https://zbmath.org/authors/?q=ai:husain.shahid"Sharifpur, Mohsen"https://zbmath.org/authors/?q=ai:sharifpur.mohsen(no abstract)Deposition pattern of drying dropletshttps://zbmath.org/1521.767272023-11-13T18:48:18.785376Z"Yang, Xiuyuan"https://zbmath.org/authors/?q=ai:yang.xiuyuan"Jiang, Zechao"https://zbmath.org/authors/?q=ai:jiang.zechao"Lyu, Peihan"https://zbmath.org/authors/?q=ai:lyu.peihan"Ding, Zhaoyu"https://zbmath.org/authors/?q=ai:ding.zhaoyu"Man, Xingkun"https://zbmath.org/authors/?q=ai:man.xingkunSummary: The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications, ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations, facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.Modeling droplet collision dynamic for Lagrangian simulation of impinging spray under high ambient pressures using an improved approachhttps://zbmath.org/1521.768642023-11-13T18:48:18.785376Z"Wei, Xiao"https://zbmath.org/authors/?q=ai:wei.xiao"Zhang, Zhenyu"https://zbmath.org/authors/?q=ai:zhang.zhenyuSummary: Spray-to-spray impingement under ambient pressures of 10--60 atm was investigated numerically and experimentally, with particular interest in illustrating the influence of droplet collision dynamic on the spray characteristic. Specially, an improved approach for collision probability prediction was proposed by taking into account the initial size and distance of colliding droplets. The numerical simulations show our approach accounts for the collisions among droplets located in the different computational cells, hence producing substantial independence of computational cell size and total parcel number. The improved approach was subsequently implemented with a recently proposed pressure-dependent collision outcome model to simulate the impinging spray characteristics, the results were compared to the widely-used O'Rourke's and Estrade et al.'s models. By implementing the improved approach with the pressure-dependent collision outcome model, our numerical simulations successfully reproduce the tendency that droplet bouncing is promoted with increasing ambient pressure, which has been fully recognized in the previous experimental and theoretical studies, however, rarely reflected in previous numerical works. Spray microcosmic characteristic was further discussed based on the numerical simulations.Investigation of nano-droplet wetting states on array micro-structured surfaces with different gravityhttps://zbmath.org/1521.768652023-11-13T18:48:18.785376Z"Xu, Bo"https://zbmath.org/authors/?q=ai:xu.bo"Zhang, Cancan"https://zbmath.org/authors/?q=ai:zhang.cancan"Chen, Zhenqian"https://zbmath.org/authors/?q=ai:chen.zhenqian"Yang, Yang"https://zbmath.org/authors/?q=ai:yang.yang.43"Cao, Qian"https://zbmath.org/authors/?q=ai:cao.qianSummary: In order to obtain the influence law and microscale mechanism of droplet wetting state in microgravity, the model of nano-droplet on array micro-structured surface with different wettability and gravity was built and simulated by molecular dynamics. In conditions of no gravity, it was found that critical point of wetting state transition was closer to weak wettability surface with the decrease of low range micro-column height. What's more, the droplet contact angle increased first and then decreased with larger micro-column height when \textit{h*}< 1.5. Under the action of gravity, the droplet Cassie state basically did not appear. The greater gravity made the droplet wetting state transition (from Cassie to Wenzel-Cassie to Wenzel) need lower requirements for surface wettability and micro-column height. Moreover, microgravity environment was conducive to droplets transition from Wenzel to Wenzel-Cassie or Cassie state, which promoting droplet drainage. Finally, a simple, effective and reliable method was put forward to judge the droplets wetting state under different gravity, with the aim of providing a technical support for controlling droplet to be in Wenzel-Cassie state under gravity.Frictional, thermal, and total entropy generation of two-phase nanofluid turbulent flow in a circular heatsink: a numerical studyhttps://zbmath.org/1521.768702023-11-13T18:48:18.785376Z"Mustafa, Jawed"https://zbmath.org/authors/?q=ai:mustafa.jawed"Abdullah, M. M."https://zbmath.org/authors/?q=ai:abdullah.m-m"Ahmad, Mohammad Zaki"https://zbmath.org/authors/?q=ai:ahmad.mohammad-zaki"Jamil, Basharat"https://zbmath.org/authors/?q=ai:jamil.basharat"Sharifpur, Mohsen"https://zbmath.org/authors/?q=ai:sharifpur.mohsen(no abstract)Broken ergodicity in magnetohydrodynamic turbulencehttps://zbmath.org/1521.769162023-11-13T18:48:18.785376Z"Shebalin, John V."https://zbmath.org/authors/?q=ai:shebalin.john-vSummary: Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as ``absolute equilibrium ensemble'' theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field \(\boldsymbol{B}_{\mathrm{o}}\). Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when \(\boldsymbol{B}_{\mathrm{o}} = \mathbf{0}\) and weakly broken when \(\boldsymbol{B}_{\mathrm{o}} \neq \mathbf{0}\). Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector \(\boldsymbol{k}\)) can occur at low values of wavenumber \(k = |\boldsymbol{k}|\), especially when \(\boldsymbol{B}_{\mathrm{o}} = \mathbf{0}\). This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber \(k\) for 3-D cases, and at either lowest or highest \(k\) for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum \(k\) in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.The collision frequency of electron-neutral-particle in weakly ionized plasmas with non-Maxwellian velocity distributionshttps://zbmath.org/1521.780042023-11-13T18:48:18.785376Z"Wang, Hong"https://zbmath.org/authors/?q=ai:wang.hong.7|wang.hong.3|wang.hong.12|wang.hong.4|wang.hong.2|wang.hong.9|wang.hong.1|wang.hong.6|wang.hong|wang.hong.5"Du, Jiulin"https://zbmath.org/authors/?q=ai:du.jiulin"Huo, Rui"https://zbmath.org/authors/?q=ai:huo.ruiSummary: The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in plasmas are accurately derived. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in plasmas. Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.Effect of the length and thickness of three constant temperature baffles on the natural convection heat transfer of nanofluid flow inside an enclosure affected by a magnetic fieldhttps://zbmath.org/1521.800142023-11-13T18:48:18.785376Z"Wang, Dan"https://zbmath.org/authors/?q=ai:wang.dan.1"Hai, Tao"https://zbmath.org/authors/?q=ai:hai.tao(no abstract)Investigation of phase change and heat transfer in water/copper oxide nanofluid enclosed in a cylindrical tank with porous medium: a molecular dynamics approachhttps://zbmath.org/1521.800162023-11-13T18:48:18.785376Z"Aljaloud, Amjad Salamah M."https://zbmath.org/authors/?q=ai:aljaloud.amjad-salamah-m"Smida, Kamel"https://zbmath.org/authors/?q=ai:smida.kamel"Ameen, Hawzhen Fateh M."https://zbmath.org/authors/?q=ai:ameen.hawzhen-fateh-m"Albedah, M. A."https://zbmath.org/authors/?q=ai:albedah.m-a"Tlili, Iskander"https://zbmath.org/authors/?q=ai:tlili.iskander(no abstract)Conserved charges in the quantum simulation of integrable spin chainshttps://zbmath.org/1521.810062023-11-13T18:48:18.785376Z"Maruyoshi, Kazunobu"https://zbmath.org/authors/?q=ai:maruyoshi.kazunobu"Okuda, Takuya"https://zbmath.org/authors/?q=ai:okuda.takuya"Pedersen, Juan W."https://zbmath.org/authors/?q=ai:pedersen.juan-w"Suzuki, Ryo"https://zbmath.org/authors/?q=ai:suzuki.ryo"Yamazaki, Masahito"https://zbmath.org/authors/?q=ai:yamazaki.masahito.1|yamazaki.masahito"Yoshida, Yutaka"https://zbmath.org/authors/?q=ai:yoshida.yutakaSummary: When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. For certain spin chains, it is possible to discretize the time evolution preserving integrability, so that an extensive set of conserved charges are exactly conserved after discretization. In this work we implement, on real quantum computers and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.A theory of quantum (statistical) measurementhttps://zbmath.org/1521.810152023-11-13T18:48:18.785376Z"Wreszinski, Walter F."https://zbmath.org/authors/?q=ai:wreszinski.walter-fSummary: We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp's theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach experiment. The number \(N\) of degrees of freedom of the measuring apparatus is such that \(N \rightarrow \infty\), justifying the adjective ``statistical'', but, in addition, and in contrast to Hepp's approach, we make a three-fold assumption: the measurement is not instantaneous, it lasts a finite amount of time and is, up to arbitrary accuracy, performed in a finite region of space, in agreement with the additional axioms proposed by Basdevant and Dalibard. It is then shown how von Neumann's ``collapse postulate'' may be avoided by a mathematically precise formulation of an argument of Gottfried, and, at the same time, Heisenberg's ``destruction of knowledge'' paradox is eliminated. The fact that no irreversibility is attached to the process of measurement is shown to follow from the author's theory of irreversibility, formulated in terms of the mean entropy, due to the latter's property of affinity.Entropy of quantum systems with linear dissipationhttps://zbmath.org/1521.810172023-11-13T18:48:18.785376Z"Kirchanov, V. S."https://zbmath.org/authors/?q=ai:kirchanov.v-s(no abstract)Diagonalization in a quantum kicked rotor model with non-analytic potentialhttps://zbmath.org/1521.810212023-11-13T18:48:18.785376Z"Shi, Yunfeng"https://zbmath.org/authors/?q=ai:shi.yunfeng"Wen, Li"https://zbmath.org/authors/?q=ai:wen.liSummary: In this paper we study the lattice quasi-periodic operators with power-law long-range hopping and meromorphic monotone potentials, and diagonalize the operators via a Nash-Moser iteration scheme. As applications, we obtain uniform power-law localization, uniform dynamical localization and Lipschitz continuity of the integrated density of states (IDS) for such operators. Our main motivation comes from investigating quantum suppression of chaos in a quantum kicked rotor model with non-analytical potential.Stationary hypergeometric solitons and their stability in a Bose-Einstein condensate with \(\mathcal{PT}\)-symmetric potentialhttps://zbmath.org/1521.810622023-11-13T18:48:18.785376Z"Bhatia, Sanjana"https://zbmath.org/authors/?q=ai:bhatia.sanjana"Goyal, Amit"https://zbmath.org/authors/?q=ai:goyal.amit"Jana, Soumendu"https://zbmath.org/authors/?q=ai:jana.soumendu"Kumar, C. N."https://zbmath.org/authors/?q=ai:kumar.c-nagarajaSummary: We report the existence of stationary nonlinear matter-waves in a trapped Bose-Einstein condensate subject to a \(\mathcal{PT}\)-symmetric Pöschl-Teller potential with a gain/loss profile. Exact nonlinear modes are obtained and their stability criteria are determined. The analysis shows that beyond a critical depth of confining potential well, the condensate wavefunction is stable against small fluctuations in the field. Analytical results obtained are in good agreement with the numerical simulation of the localized modes in the \(\mathcal{PT}\) symmetry regime. Employing the isospectral hamiltonian technique of supersymmetric quantum mechanics, we demonstrate a mechanism to control the shape of the Pöschl-Teller well and hence the intensity of the localized modes. Most importantly, our results reveal that even with a small fluctuation present in the trapping potential bearing dissipation, the system is robust enough to support stable propagation of nonlinear modes.Exact solution of the \(q\)-deformed \(D_3^{(1)}\) vertex model with open boundarieshttps://zbmath.org/1521.810942023-11-13T18:48:18.785376Z"Li, Guang-Liang"https://zbmath.org/authors/?q=ai:li.guangliang"Cao, Junpeng"https://zbmath.org/authors/?q=ai:cao.junpeng"Qiao, Yi"https://zbmath.org/authors/?q=ai:qiao.yi"Yang, Wen-Li"https://zbmath.org/authors/?q=ai:yang.wenliSummary: In this paper, we study the exact solution of the \(q\)-deformed \(D_3^{(1)}\) quantum lattice model with non-diagonal open boundary condition. We demonstrate the crossing symmetry of the transfer matrix and obtain the quantum determinant. We construct the independent transfer matrix fusion identities and show that the fusion processes can be closed. Based on the fusion hierarchies and polynomial analysis, we obtain the inhomogeneous \(T\)-\(Q\) relations, exact energy spectrum and Bethe ansatz equations of the system.Thermodynamic Bethe ansatz past turning points: the (elliptic) sinh-Gordon modelhttps://zbmath.org/1521.811042023-11-13T18:48:18.785376Z"Córdova, Lucía"https://zbmath.org/authors/?q=ai:cordova.lucia"Negro, Stefano"https://zbmath.org/authors/?q=ai:negro.stefano"Schaposnik Massolo, Fidel I."https://zbmath.org/authors/?q=ai:schaposnik-massolo.fidel-iSummary: We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized \(\mathrm{T}\bar{\mathrm{T}}\) deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number \(k\) of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As \(k\rightarrow\infty\) the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the \(S\)-matrices describing the \(\Phi_{1, 3}\) integrable deformation of non-unitary minimal models \(\mathcal{M}_{2, 2n+3}\).Kondo line defects and affine Gaudin modelshttps://zbmath.org/1521.811052023-11-13T18:48:18.785376Z"Gaiotto, Davide"https://zbmath.org/authors/?q=ai:gaiotto.davide"Lee, Ji Hoon"https://zbmath.org/authors/?q=ai:lee.jihoon.2"Vicedo, Benoît"https://zbmath.org/authors/?q=ai:vicedo.benoit"Wu, Jingxiang"https://zbmath.org/authors/?q=ai:wu.jingxiangSummary: We describe the relation between integrable Kondo problems in products of chiral SU(2) WZW models and affine SU(2) Gaudin models. We propose a full ODE/IM solution of the spectral problem for these models.Quantum transport efficiency in noisy random-removal and small-world networkshttps://zbmath.org/1521.811242023-11-13T18:48:18.785376Z"Kurt, Arzu"https://zbmath.org/authors/?q=ai:kurt.arzu"Rossi, Matteo A. C."https://zbmath.org/authors/?q=ai:rossi.matteo-a-c"Piilo, Jyrki"https://zbmath.org/authors/?q=ai:piilo.jyrkiSummary: We report the results of an in-depth study of the role of graph topology on quantum transport efficiency in random removal and Watts-Strogatz networks. By using four different environmental models---noiseless, driven by classical random telegraph noise (RTN), thermal quantum bath, and bath + RTN---we compare the role of the environment and of the change in network topology in determining the quantum transport efficiency. We find that small and specific changes in network topology is more effective in causing large change in efficiency compared to that achievable by environmental manipulations for both network classes. Furthermore, we have found that noise dependence of transport efficiency in Watts-Strogatz networks can be categorized into six classes. In general, our results highlight the interplay that network topology and environment models play in quantum transport, and pave the way for transport studies for networks of increasing size and complexity---when going beyond so far often used few-site transport systems.Correlation decay and Markovianity in open systemshttps://zbmath.org/1521.811272023-11-13T18:48:18.785376Z"Merkli, Marco"https://zbmath.org/authors/?q=ai:merkli.marcoSummary: A finite quantum system S is coupled to a thermal, bosonic reservoir R. Initial SR states are possibly correlated, obtained by applying a quantum operation taken from a large class, to the uncoupled equilibrium state. We show that the full system-reservoir dynamics is given by a Markovian term plus a correlation term, plus a remainder small in the coupling constant \(\lambda\) uniformly for all times \(t\ge 0\). The correlation term decays polynomially in time, at a speed independent of \(\lambda\). After this, the Markovian term becomes dominant, where the system evolves according to the completely positive, trace-preserving semigroup generated by the Davies generator, while the reservoir stays stationary in equilibrium. This shows that (a) after initial SR correlations decay, the SR dynamics enters a regime where both the Born and Markov approximations are valid, and (b) the reduced system dynamics is Markovian for all times, even for correlated SR initial states.Non-equilibrium dynamics of a scalar field with quantum backreactionhttps://zbmath.org/1521.811972023-11-13T18:48:18.785376Z"Kainulainen, Kimmo"https://zbmath.org/authors/?q=ai:kainulainen.kimmo"Koskivaara, Olli"https://zbmath.org/authors/?q=ai:koskivaara.olliSummary: We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow the decay and thermalization of a scalar field from an initial cold state with all energy stored in the potential, into a fully thermalized system with a finite temperature. We identify the non-perturbative processes of parametric resonance and spinodal instability taking place during the reheating stage. In particular we study the unstable modes in the region where the vacuum 1PI effective action becomes complex and show that such spinodal modes can have a dramatic effect on the evolution of the one-point function. Our methods can be easily adapted to simulate reheating at the end of inflation.Bethe ansatz for quantum-deformed stringshttps://zbmath.org/1521.812362023-11-13T18:48:18.785376Z"Seibold, Fiona K."https://zbmath.org/authors/?q=ai:seibold.fiona-k"Sfondrini, Alessandro"https://zbmath.org/authors/?q=ai:sfondrini.alessandroSummary: Two distinct \(\eta\)-deformations of strings on \(\mathrm{AdS}_5\times\mathrm{S}^5\) can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare their conjectured all-loop worldsheet S matrices and derive the corresponding Bethe equations. We find that, while the S matrices are apparently different, they lead to the same Bethe equations. Moreover, in either case the eigenvalues of the transfer matrix, which encode the conserved charges of each system, also coincide. We conclude that the integrable structure underlying the two constructions is essentially the same. Finally, we write down the full Bethe-Yang equations describing the asymptotic spectrum of the superstring background.Breaking rotations without violating the KSS viscosity boundhttps://zbmath.org/1521.812502023-11-13T18:48:18.785376Z"Baggioli, Matteo"https://zbmath.org/authors/?q=ai:baggioli.matteo"Cremonini, Sera"https://zbmath.org/authors/?q=ai:cremonini.sera"Early, Laura"https://zbmath.org/authors/?q=ai:early.laura"Li, Li"https://zbmath.org/authors/?q=ai:li.li.22"Sun, Hao-Tian"https://zbmath.org/authors/?q=ai:sun.hao-tianSummary: We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for \(\eta/s\), which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of \(\eta/s\) in the broken phase, competing against the effects of spontaneous symmetry breaking. However, \(\eta/s\) always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, \(1/4\pi\). This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of \(\eta/s\) at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.Quantum spectral curve for \(\mathrm{AdS}_3/\mathrm{CFT}_2\): a proposalhttps://zbmath.org/1521.812512023-11-13T18:48:18.785376Z"Cavaglià, Andrea"https://zbmath.org/authors/?q=ai:cavaglia.andrea"Gromov, Nikolay"https://zbmath.org/authors/?q=ai:gromov.nikolay-a"Stefański, Bogdan jun."https://zbmath.org/authors/?q=ai:stefanski.bogdan-jun"Torrielli, Alessandro"https://zbmath.org/authors/?q=ai:torrielli.alessandroSummary: We conjecture the Quantum Spectral Curve equations for string theory on \(\mathrm{AdS}_3 \times S^3 \times T^4\) with RR charge and its \(\mathrm{CFT}_2\) dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known \(\mathrm{AdS}_5\) and \(\mathrm{AdS}_4\) cases, but contains a critical new feature -- the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.Impurity effect on hysteric magnetoconductance: holographic approachhttps://zbmath.org/1521.812622023-11-13T18:48:18.785376Z"Kim, Kyung Kiu"https://zbmath.org/authors/?q=ai:kim.kyung-kiu"Kim, Keun-Young"https://zbmath.org/authors/?q=ai:kim.keun-young"Sin, Sang-Jin"https://zbmath.org/authors/?q=ai:sin.sang-jin"Seo, Yunseok"https://zbmath.org/authors/?q=ai:seo.yunseokSummary: In this paper we study a hysteric phase transition from weak localization phase to hysteric magnetoconductance phase using gauge/gravity duality. This hysteric phase is triggered by a spontaneous magnetization related to \(\mathbb{Z}_2\) symmetry and time reversal symmetry in a \(2+1\) dimensional system with momentum relaxation. We derive thermoelectric conductivity formulas describing non-hysteric and hysteric phases. At low temperatures, this magnetoconductance shows similar phase transitions of topological insulator surface states. We also obtain hysteresis curves of Seebeck coefficient and Nernst signal. It turns out that our impurity parameter changes magnetic properties of the dual system. This is justified by showing increasing susceptibility and the spontaneous magnetization with increasing impurity parameter.Instability of holographic superfluids in optical latticehttps://zbmath.org/1521.812742023-11-13T18:48:18.785376Z"Yang, Peng"https://zbmath.org/authors/?q=ai:yang.peng"Li, Xin"https://zbmath.org/authors/?q=ai:li.xin.32"Tian, Yu"https://zbmath.org/authors/?q=ai:tian.yuSummary: The instability of superfluids in optical lattice has been investigated using the holographic model. The static and steady flow solutions are numerically obtained from the static equations of motion and the solutions are described as Bloch waves with different Bloch wave vector \(k\). Based on these Bloch waves, the instability is investigated at two levels. At the linear perturbation level, we show that there is a critical \(k_c\) above which the superflow is unstable. At the fully nonlinear level, the intermediate state and final state of unstable superflow are identified through numerical simulation of the full equations of motion. The results show that during the time evolution, the unstable superflow will undergo a chaotic state with soliton generation. The system will settle down to a stable state with \(k < k_c\) eventually, with a smaller current and a larger condensate.A holographic superfluid symphonyhttps://zbmath.org/1521.812812023-11-13T18:48:18.785376Z"Areán, Daniel"https://zbmath.org/authors/?q=ai:arean.daniel"Baggioli, Matteo"https://zbmath.org/authors/?q=ai:baggioli.matteo"Grieninger, Sebastian"https://zbmath.org/authors/?q=ai:grieninger.sebastian"Landsteiner, Karl"https://zbmath.org/authors/?q=ai:landsteiner.karlSummary: We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.Entanglement entropy of inhomogeneous XX spin chains with algebraic interactionshttps://zbmath.org/1521.813052023-11-13T18:48:18.785376Z"Finkel, Federico"https://zbmath.org/authors/?q=ai:finkel.federico"González-López, Artemio"https://zbmath.org/authors/?q=ai:gonzalez-lopez.artemioSummary: We introduce a family of inhomogeneous XX spin chains whose squared couplings are a polynomial of degree at most four in the site index. We show how to obtain an asymptotic approximation for the Rényi entanglement entropy of all such chains in a constant magnetic field at half filling by exploiting their connection with the conformal field theory of a massless Dirac fermion in a suitably curved static background. We study the above approximation for three particular chains in the family, two of them related to well-known quasi-exactly solvable quantum models on the line and the third one to classical Krawtchouk polynomials, finding an excellent agreement with the exact value obtained numerically when the Rényi parameter \(\alpha\) is less than one. When \(\alpha \geqslant 1\) we find parity oscillations, as expected from the homogeneous case, and show that they are very accurately reproduced by a modification of the Fagotti-Calabrese formula. We have also analyzed the asymptotic behavior of the Rényi entanglement entropy in the non-standard situation of arbitrary filling and/or inhomogeneous magnetic field. Our numerical results show that in this case a block of spins at each end of the chain becomes disentangled from the rest. Moreover, the asymptotic approximation for the case of half filling and constant magnetic field, when suitably rescaled to the region of non-vanishing entropy, provides a rough approximation to the entanglement entropy also in this general case.Finite size spectrum of the staggered six-vertex model with \(\mathrm{U_q}(\mathfrak{sl}(2))\)-invariant boundary conditionshttps://zbmath.org/1521.813082023-11-13T18:48:18.785376Z"Frahm, Holger"https://zbmath.org/authors/?q=ai:frahm.holger"Gehrmann, Sascha"https://zbmath.org/authors/?q=ai:gehrmann.saschaSummary: The finite size spectrum of the critical \(\mathbb{Z}_2\)-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact \(\mathrm{SU}(2, \mathbb{R})/\mathrm{U}(1)\) Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.Hexagonalization of fishnet integrals. I: Mirror excitationshttps://zbmath.org/1521.813222023-11-13T18:48:18.785376Z"Olivucci, Enrico"https://zbmath.org/authors/?q=ai:olivucci.enricoSummary: In this paper we consider a conformal invariant chain of \(L\) sites in the unitary irreducible representations of the group \(\mathrm{SO}(1, 5)\). The \(k\)-th site of the chain is defined by a scaling dimension \(\Delta_k\) and spin numbers \(\frac{\ell_k}{2}\), \(\frac{\dot{\ell}_k}{2}\) The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice ``fishnet'' integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the \textit{mirror excitations} of the lattice: particles with SO(4) internal symmetry that scatter according to an integrable factorized \(\mathcal{S}\)-matrix in \((1 + 1)\) dimensionsTopological recursion and uncoupled BPS structures. II: Voros symbols and the \(\tau\)-functionhttps://zbmath.org/1521.813942023-11-13T18:48:18.785376Z"Iwaki, Kohei"https://zbmath.org/authors/?q=ai:iwaki.kohei"Kidwai, Omar"https://zbmath.org/authors/?q=ai:kidwai.omarSummary: We continue our study of the correspondence between BPS structures and topological recursion in the uncoupled case, this time from the viewpoint of quantum curves. For spectral curves of hypergeometric type, we show the Borel-resummed Voros symbols of the corresponding quantum curves solve Bridgeland's ``BPS Riemann-Hilbert problem''. In particular, they satisfy the required jump property in agreement with the generalized definition of BPS indices \(\Omega\) in our previous work. Furthermore, we observe the Voros coefficients define a closed one-form on the parameter space, and show that (log of) Bridgeland's \(\tau\)-function encoding the solution is none other than the corresponding potential, up to a constant. When the quantization parameter is set to a special value, this agrees with the Borel sum of the topological recursion partition function \(Z_\mathrm{TR}\), up to a simple factor.
For Part I, see [the authors, Adv. Math. 398, Article ID 108191, 54 p. (2022; Zbl 1486.81157)].Notes on index of quantum integrabilityhttps://zbmath.org/1521.814162023-11-13T18:48:18.785376Z"Tian, Jia"https://zbmath.org/authors/?q=ai:tian.jia"Hou, Jue"https://zbmath.org/authors/?q=ai:hou.jue"Chen, Bin"https://zbmath.org/authors/?q=ai:chen.bin.2Summary: A quantum integrability index was proposed in [\textit{S. Komatsu} et al., SciPost Phys. 7, Paper No. 65, 21 p. (2019; \url{doi:10.21468/SciPostPhys.7.5.065})]. It systematizes the Goldschmidt and Witten's operator counting argument [\textit{Y. Y. Goldschmidt} and \textit{E. Witten}, Phys. Lett., B 91, No. 3--4, 392--396 (1980; \url{doi:10.1016/0370-2693(80)91004-7})] by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models \(SU(N)/SO(N)\) and \(SO(2N)/SO(N)\times SO(N)\). The indexes of these theories are all non-positive except for the case of \(SO(4)/SO(2)\times SO(2)\). Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the \(\mathbb{CP}^N\) model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.Three-point functions in ABJM and Bethe ansatzhttps://zbmath.org/1521.814172023-11-13T18:48:18.785376Z"Yang, Peihe"https://zbmath.org/authors/?q=ai:yang.peihe"Jiang, Yunfeng"https://zbmath.org/authors/?q=ai:jiang.yunfeng"Komatsu, Shota"https://zbmath.org/authors/?q=ai:komatsu.shota"Wu, Jun-Bao"https://zbmath.org/authors/?q=ai:wu.junbaoSummary: We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.The role of colour flows in matrix element computations and Monte Carlo simulationshttps://zbmath.org/1521.814592023-11-13T18:48:18.785376Z"Frixione, Stefano"https://zbmath.org/authors/?q=ai:frixione.stefano"Webber, Bryan R."https://zbmath.org/authors/?q=ai:webber.bryan-rSummary: We discuss how colour flows can be used to simplify the computation of matrix elements, and in the context of parton shower Monte Carlos with accuracy beyond leading-colour. We show that, by systematically employing them, the results for tree-level matrix elements and their soft limits can be given in a closed form that does not require any colour algebra. The colour flows that we define are a natural generalization of those exploited by existing Monte Carlos; we construct their representations in terms of different but conceptually equivalent quantities, namely colour loops and dipole graphs, and examine how these objects may help to extend the accuracy of Monte Carlos through the inclusion of subleading-colour effects. We show how the results that we obtain can be used, with trivial modifications, in the context of QCD+QED simulations, since we are able to put the gluon and photon soft-radiation patterns on the same footing. We also comment on some peculiar properties of gluon-only colour flows, and their relationships with established results in the mathematics of permutations.Low-dimensional life of critical Anderson electronhttps://zbmath.org/1521.814612023-11-13T18:48:18.785376Z"Horváth, Ivan"https://zbmath.org/authors/?q=ai:horvath.ivan"Markoš, Peter"https://zbmath.org/authors/?q=ai:markos.peterSummary: We show that critical Anderson electron in 3 dimensions is present in its spatial effective support, which was recently determined to be a region of fractal dimension \(\approx 8/3\), with probability 1 in infinite volume. Hence, its physics is fully confined to space of this lower dimension. Stated differently, effective description of space occupied by critical Anderson electron becomes a full description in infinite volume. We then show that it is a general feature of the effective counting dimension underlying these concepts, that its subnominal value implies an exact description by effective support.Detailed comparison of renormalization scale-setting procedures based on the principle of maximum conformalityhttps://zbmath.org/1521.814622023-11-13T18:48:18.785376Z"Huang, Xu-Dong"https://zbmath.org/authors/?q=ai:huang.xudong"Yan, Jiang"https://zbmath.org/authors/?q=ai:yan.jiang"Ma, Hong-Hao"https://zbmath.org/authors/?q=ai:ma.hong-hao"Di Giustino, Leonardo"https://zbmath.org/authors/?q=ai:di-giustino.leonardo"Shen, Jian-Ming"https://zbmath.org/authors/?q=ai:shen.jian-ming"Wu, Xing-Gang"https://zbmath.org/authors/?q=ai:wu.xing-gang"Brodsky, Stanley J."https://zbmath.org/authors/?q=ai:brodsky.stanley-jSummary: The \textit{Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality'' \((\mathrm{PMC}_\infty)\). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities \(R_{e^+ e^-}\), \(R_\tau\), and \(\Gamma(H\to b\overline{b})\) up to four-loop pQCD corrections.
The PMCs approach determines an overall effective running coupling \(\alpha_s(Q)\) by the recursive use of the renormalization group equation, whose argument \(Q\) represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.Intermediate symmetric construction of transformation between anyon and Gentile statisticshttps://zbmath.org/1521.814872023-11-13T18:48:18.785376Z"Shen, Yao"https://zbmath.org/authors/?q=ai:shen.yao"Zhang, Fu-Lin"https://zbmath.org/authors/?q=ai:zhang.fulinSummary: Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between Bose-Einstein and Fermi-Dirac statistics. The second quantization of Gentile statistics shows a lot of advantages. According to the symmetry requirement of the wave function and the property of braiding, we give the general construction of transformation between anyon and Gentile statistics. In other words, we introduce the second quantization form of anyons in an easier way. This construction is a correspondence between two fractional statistics and gives a new description of anyon. Basic relations of second quantization operators, the coherent state and Berry phase are also discussed.A close-up to the bond-breaking and bond-forming using information theoryhttps://zbmath.org/1521.814952023-11-13T18:48:18.785376Z"Flores-Gallegos, N."https://zbmath.org/authors/?q=ai:flores-gallegos.nelsonSummary: In this work, we analyzed the chemical reaction, \(\mathrm{CH}_4 + \mathrm{H}^- \longrightarrow \mathrm{CH}_4 + \mathrm{H}^-\), using the concept of information channel, which consists in to quantify the amount of information that the system can transfer and receive, to carry out such measures, we used Shannon's entropy defined in position and momentum spaces, the interpretation of the results obtained was also completed by the analysis of Fisher's entropy in position and momentum spaces; our results, permitted to analyze with certain detail how are carried out the process of bond-forming and bond-breaking of the reaction \(\mathrm{CH}_4 + \mathrm{H}^-\).Reduced fluctuations for bosons in a double wellhttps://zbmath.org/1521.815012023-11-13T18:48:18.785376Z"Olgiati, Alessandro"https://zbmath.org/authors/?q=ai:olgiati.alessandroSummary: We review two recent results on the ground state properties of bosonic systems trapped by a double well external potential. In the limit of a large number of particles and large separation between the wells, we prove that fluctuations in the number of particles occupying each single-well low-energy mode occur at a reduced scale with respect to \(\sqrt{N}\), the latter being the typical prediction of the central limit theorem. This signals the breakdown of the independent and uncorrelated particle picture of standard Bose-Einstein condensation and the emergence of an interaction-driven correlated phase in the ground state.
{\copyright 2022 American Institute of Physics}Optical pulses in a superlattice-based photonic crystal under the conditions of an optical cavityhttps://zbmath.org/1521.815042023-11-13T18:48:18.785376Z"Dvuzhilova, Yu. V."https://zbmath.org/authors/?q=ai:dvuzhilova.yu-v"Dvuzhilov, I. S."https://zbmath.org/authors/?q=ai:dvuzhilov.i-s"Belonenko, M. B."https://zbmath.org/authors/?q=ai:belonenko.mikhail-b(no abstract)Spectral structure of two-mode Rabi-Stark modelhttps://zbmath.org/1521.815062023-11-13T18:48:18.785376Z"Liu, Yan"https://zbmath.org/authors/?q=ai:liu.yan.34"Qiu, Fangcheng"https://zbmath.org/authors/?q=ai:qiu.fangcheng"Liu, Ronghai"https://zbmath.org/authors/?q=ai:liu.ronghai"Ma, Jinying"https://zbmath.org/authors/?q=ai:ma.jinying"Yan, Zhanyuan"https://zbmath.org/authors/?q=ai:yan.zhanyuanSummary: The analytical solutions of the two-mode Rabi-Stark model (tmRSM) are obtained by using the Bogoliubov operators approach in \(su(1, 1)\) Lie algebra space, which fit the exact numerical results well. The structure of the energy spectra is related to many fundamental physics characters such as symmetry, quantum phase transition
(QPT), spectral collapse etc. In this paper, the spectral structure of tmRSM is discussed analytically. The regular energy spectra are given by the zeros of the G-function, and the poles appearing in the G-function are responsible for the exceptional solutions. The double degenerate exceptional solutions could be predicted by discussing the divergence of the coefficients in the G-function. If the numerator and denominator of \(\Omega_n\) vanish, the lowest double degenerate exceptional solutions for the \(n\)th energy levels would be located, including the first-order QPT point, the corresponding energy \((-\Delta/U)\) is independent of the coupling strength and the energy level, even independent of the Bargmann index \(q\). While, the nondegenerate exceptional solutions can be reproduced by the nondegenerate exceptional G-functions, the results show that more nondegenerate exceptional solutions would be found in the subspace with larger \(q\). Then, the regular solution and two kinds of exceptional Juddian solutions of tmRSM are accurately located. The spectral collapse energy are dependent on the strength of Stark coupling and the frequency of two-level system, and Stark coupling could results in the limit of \(E_0\) pole line is higher than that of \(E_n\) pole lines, which may cause more energy levels separate from the collapse energy.Interband multiphoton absorption of polarized radiation and its linear circular dichroism in semiconductors in the Kane approximationhttps://zbmath.org/1521.815072023-11-13T18:48:18.785376Z"Rasulov, R. Ya."https://zbmath.org/authors/?q=ai:rasulov.r-ya"Rasulov, V. R."https://zbmath.org/authors/?q=ai:rasulov.v-r"Kuchkarov, M. Kh."https://zbmath.org/authors/?q=ai:kuchkarov.m-kh"Eshboltaev, I. M."https://zbmath.org/authors/?q=ai:eshboltaev.i-m(no abstract)Quantum statistical mechanics in classical phase spacehttps://zbmath.org/1521.820012023-11-13T18:48:18.785376Z"Attard, Phil"https://zbmath.org/authors/?q=ai:attard.philPublisher's description: Quantum and classical results are often presented as being dependent upon separate postulates as if the two are distinct and unrelated, and there is little attempt to show how the quantum implies the classical. The transformation to classical phase space gives researchers access to a range of algorithms derived from classical statistical mechanics that promise results on much more favourable numerical terms. Quantum Statistical Mechanics in Classical Phase Space offers not just a new computational approach to condensed matter systems, but also a unique conceptual framework for understanding the quantum world and collective molecular behaviour. A formally exact transformation, this revolutionary approach goes beyond the quantum perturbation of classical condensed matter to applications that lie deep in the quantum regime. It offers scalable computational algorithms and tractable approximations tailored to specific systems. Concrete examples serve to validate the general approach and demonstrate new insights. For example, the computer simulations and analysis of the \(\lambda\)-transition in liquid helium provide a new molecular-level explanation of Bose-Einstein condensation and a quantitative theory for superfluid flow. The intriguing classical phase space formulation in this book offers students and researchers a range of new computational algorithms and analytic approaches. It offers not just an efficient computational approach to quantum condensed matter systems, but also an exciting perspective on how the classical world that we observe emerges from the quantum mechanics that govern the behaviour of atoms and molecules. The applications, examples, and physical insights foreshadow new discoveries in quantum condensed matter systems.Statistical mechanics: theory and molecular simulationhttps://zbmath.org/1521.820022023-11-13T18:48:18.785376Z"Tuckerman, Mark E."https://zbmath.org/authors/?q=ai:tuckerman.mark-eFrom the publisher's description: New to this Edition:
\begin{itemize}
\item Includes updated content on free-energy methods to reflect the current landscape of rare-event sampling methods
\item Discussion of multiple time-step algorithms has been extended to include new resonance-free techniques
\item Use of functional calculus to provide a new approach for deriving ensemble distributions
\item Includes discussion of the Potential Distribution and Henderson Theorems
\end{itemize}
See the review of the first edition in [Zbl 1232.82002].Root patterns and energy spectra of quantum integrable systems without U(1) symmetry: the antiperiodic \textit{XXZ} spin chainhttps://zbmath.org/1521.820032023-11-13T18:48:18.785376Z"Le, Xiong"https://zbmath.org/authors/?q=ai:le.xiong"Qiao, Yi"https://zbmath.org/authors/?q=ai:qiao.yi"Cao, Junpeng"https://zbmath.org/authors/?q=ai:cao.junpeng"Yang, Wen-Li"https://zbmath.org/authors/?q=ai:yang.wenli"Shi, Kangjie"https://zbmath.org/authors/?q=ai:shi.kangjie"Wang, Yupeng"https://zbmath.org/authors/?q=ai:wang.yupengSummary: Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without U(1) symmetry, their spectra are usually given by inhomogeneous \(T\)-\(Q\) relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic \textit{XXZ} spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.Ising percolation in the hyperbolic planehttps://zbmath.org/1521.820042023-11-13T18:48:18.785376Z"Li, Zhongyang"https://zbmath.org/authors/?q=ai:li.zhongyang|li.zhongyang.1Summary: We study infinite ``\(+\)'' or ``\(-\)'' clusters for an Ising model on an connected, transitive, non-amenable, planar, one-ended graph \(G\) with finite vertex degree. If the critical percolation probability \(p_c^{site}\) for the independent identically distributed (IID). Bernoulli site percolation on \(G\) is less than \(\frac{1}{2}\), we find an explicit region for the coupling constant of the Ising model such that there are infinitely many infinite ``\(+\)''-clusters and infinitely many infinite ``\(-\)''-clusters, while the random cluster representation of the Ising model has no infinite 1-clusters. If \(p_c^{site} > \frac{1}{2}\), we obtain a lower bound for the critical probability in the random cluster representation of the Ising model in terms of \(p_c^{site}\). We also obtain an explicit region for the coupling constant when the XOR Ising model (the product of two IID Ising models) does not have a unique infinite contour a.s. and an explicit region for the coupling constant when the XOR Ising model has infinitely many infinite ``\(+\)''-clusters and infinitely many infinite ``\(-\)''-clusters.
{\copyright 2023 American Institute of Physics}The \(p\)-adic Ising model in an external field on a Cayley tree: periodic Gibbs measureshttps://zbmath.org/1521.820052023-11-13T18:48:18.785376Z"Mukhamedov, F. M."https://zbmath.org/authors/?q=ai:mukhamedov.farruh-m"Rahmatullaev, M. M."https://zbmath.org/authors/?q=ai:rahmatullaev.muzaffar"Tukhtabaev, A. M."https://zbmath.org/authors/?q=ai:tukhtabaev.a-m"Mamadjonov, R."https://zbmath.org/authors/?q=ai:mamadjonov.rSummary: We consider the generalized Gibbs measures corresponding to the \(p\)-adic Ising model in an external field on the Cayley tree of order two. It is established that if \(p\equiv 1 \pmod 4\), then there exist three translation-invariant and two \(G_2^{(2)} \)-periodic non-translation-invariant \(p\)-adic generalized Gibbs measures. It becomes clear that if \(p\equiv 3\pmod 4\), \(p\neq3\), then one can find only one translation-invariant \(p\)-adic generalized Gibbs measure. Moreover, the considered model also exhibits chaotic behavior if \(|\eta-1|_p<|\theta-1|_p\) and \(p\equiv 1\pmod 4\). It turns out that even without \(|\eta-1|_p<|\theta-1|_p\), one could establish the existence of 2-periodic renormalization-group solutions when \(p\equiv 1\pmod 4\). This allows us to show the existence of a phase transition.Cluster perturbation theory for the Hubbard model: the pinning of chemical potentialhttps://zbmath.org/1521.820062023-11-13T18:48:18.785376Z"Nikolaev, Sergeĭ V."https://zbmath.org/authors/?q=ai:nikolaev.sergei-v"Ovchinnikov, Sergeĭ G."https://zbmath.org/authors/?q=ai:ovchinnikov.sergei-gSummary: In this paper we study the single-band two-dimensional Hubbard model in the framework of the cluster perturbation theory. Consideration is limited to nearest-neighbor approximation. The original two-dimensional square lattice is divided into clusters of \(2\times2\), forming a square superlattice. The complete set of eigenvectors and eigenvalues of a single cluster is determined by exact diagonalization method. On this basis, we construct X-operators, through which overrides the Hamiltonian of the problem. The spectral function is computed within the Hubbard-I approximation. This function allows to explore the distribution of spectral weight of the quasiparticles in the Hubbard subbands. The effect of the in-gap states at the pinning of the chemical potential at low concentrations of holes is explored.Dyson diffusion on a curved contourhttps://zbmath.org/1521.820072023-11-13T18:48:18.785376Z"Zabrodin, A. V."https://zbmath.org/authors/?q=ai:zabrodin.anton-vSummary: We define the Dyson diffusion process on a curved smooth closed contour in the plane and derive the Fokker-Planck equation for the probability density. Its stationary solution is shown to be the Boltzmann weight for the logarithmic gas confined on the contour.Integration of the two-dimensional Heisenberg model by methods of differential geometryhttps://zbmath.org/1521.820082023-11-13T18:48:18.785376Z"Borisov, A. B."https://zbmath.org/authors/?q=ai:borisov.aleksandr-borisovich|borisov.adrijan-varbanovSummary: The methods of classical differential geometry are used to integrate the two-dimensional Heisenberg model. After the hodograph transformation, the model equations are written in terms of the metric tensor associated with a curvilinear coordinate system and its derivatives. It is shown that their general solution describes all previously known exact solutions except a flat vortex. A new type of vortex structure, a ``vortex strip,'' is predicted and analyzed in two-dimensional ferromagnets. Its typical properties are the finite dimensions of the domain of definition, the finiteness of the total energy, and the absence of a vortex core in the presence of a vortex structure.Exact solution of an anisotropic \(J_1\)-\(J_2\) model with the Dzyloshinsky-Moriya interactions at boundarieshttps://zbmath.org/1521.820092023-11-13T18:48:18.785376Z"Cao, Yusong"https://zbmath.org/authors/?q=ai:cao.yusong"Wang, Jian"https://zbmath.org/authors/?q=ai:wang.jian.55"Qiao, Yi"https://zbmath.org/authors/?q=ai:qiao.yi"Cao, Junpeng"https://zbmath.org/authors/?q=ai:cao.junpeng"Yang, Wen-Li"https://zbmath.org/authors/?q=ai:yang.wenliSummary: We propose a method to construct new quantum integrable models. As an example, we construct an integrable anisotropic quantum spin chain which includes the nearest-neighbor, next-nearest-neighbor and chiral three-spin couplings. It is shown that the boundary fields can enhance the anisotropy of the first and last bonds, and can induce the Dzyloshinsky-Moriya interactions along the \(z\)-direction at the boundaries. By using the algebraic Bethe ansatz, we obtain the exact solution of the system. The energy spectrum of the system and the associated Bethe ansatz equations are given explicitly. The method provided in this paper is universal and can be applied to constructing other exactly solvable models with certain interesting interactions.Phase transitions of two spin-1/2 Baxter-Wu layers coupled with Ising-type interactionshttps://zbmath.org/1521.820102023-11-13T18:48:18.785376Z"Liu, Wei"https://zbmath.org/authors/?q=ai:liu.wei.11|liu.wei.38|liu.wei.55|liu.wei.10|liu.wei.28|liu.wei.12|liu.wei.32|liu.wei.36|liu.wei.77|liu.wei.6|liu.wei.17|liu.wei.35|liu.wei.30|liu.wei.25|liu.wei.8|liu.wei.20|liu.wei|liu.wei.47|liu.wei.54|liu.wei.45|liu.wei.58|liu.wei.19|liu.wei.18|liu.wei.29|liu.wei.27|liu.wei.22|liu.wei.2|liu.wei.7|liu.wei.24|liu.wei.16|liu.wei.50|liu.wei.23|liu.wei.34|liu.wei.40|liu.wei.5|liu.wei.13"Yan, Zhengxin"https://zbmath.org/authors/?q=ai:yan.zhengxin"Wang, Yixian"https://zbmath.org/authors/?q=ai:wang.yixianSummary: Using a Monte Carlo simulation and the single histogram reweighting technique, we study the critical behaviors and phase transitions of the Baxter-Wu (BW) model on a two-layer triangular lattice with Ising-type interlayer couplings. Via the finite-size analysis, we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings. The data for the repulsive interlayer coupling suggest continuous transitions, and the critical behaviors are the same as those of the 2D BW model, belonging to the four-state Potts universality class. The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak first-order phase transitions. The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model.On the existence of critical exponents for self-avoiding walkshttps://zbmath.org/1521.820112023-11-13T18:48:18.785376Z"Guttmann, Anthony J."https://zbmath.org/authors/?q=ai:guttmann.anthony-john"Jensen, Iwan"https://zbmath.org/authors/?q=ai:jensen.iwanSummary: We describe some ideas of \textit{J. M. Hammersley} [Proc. Camb. Philos. Soc. 57, 516--523 (1961; Zbl 0122.36501)] for proving the existence of critical exponents for two-dimensional self-avoiding walks and provide numerical evidence for their correctness.Renormalization-group analysis of 1D Hubbard modelhttps://zbmath.org/1521.820122023-11-13T18:48:18.785376Z"Lobach, Kseniya A."https://zbmath.org/authors/?q=ai:lobach.kseniya-a"Ovchinnikov, Sergeĭ G."https://zbmath.org/authors/?q=ai:ovchinnikov.sergei-gSummary: Ground state energy of 1D Hubbard model is obtained using a real-space renormalization-group tehnique. We study half-field Hubbard model with nearest-neighbor hopping.Erratum to: ``Small mass limit in mean field theory for stochastic \(N\) particle system''https://zbmath.org/1521.820132023-11-13T18:48:18.785376Z"Wang, Wei"https://zbmath.org/authors/?q=ai:wang.wei.15"Lv, Guangying"https://zbmath.org/authors/?q=ai:lv.guangying"Wei, Jinglong"https://zbmath.org/authors/?q=ai:wei.jinglongFrom the text: The proof for the mean filed limit as \(N\to +\infty\) in Sec. III of our paper [ibid. 63, No. 8, Article ID 083302, 10 p. (2022; Zbl 1509.82052)] is incorrect as we do not have a uniform estimate for \(\int_0^t \|\dot{\eta^\epsilon_i}(s)\|^2_{\mathbb{R}^d}ds\). The correct proof is given.Localization for random quasi-one-dimensional modelshttps://zbmath.org/1521.820142023-11-13T18:48:18.785376Z"Boumaza, H."https://zbmath.org/authors/?q=ai:boumaza.hakimSummary: In this Review Article, we review the results of Anderson localization for different random families of operators that enter the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and mathematical points of view. From the Anderson-Bernoulli conjecture in dimension 2, we justify the introduction of quasi-one-dimensional models. Then, we present different types of these models: the Schrödinger type in the discrete and continuous cases, the unitary type, the Dirac type, and the point interaction type. We present tools coming from the study of dynamical systems in dimension one: the transfer matrix formalism, the Lyapunov exponents, and the Furstenberg group. We then prove a criterion of localization for quasi-one-dimensional models of Schrödinger type involving only geometric and algebraic properties of the Furstenberg group. Then, we review results of localization, first for Schrödinger-type models and then for unitary type models. Each time, we reduce the question of localization to the study of the Furstenberg group and show how to use more and more refined algebraic criteria to prove the needed properties of this group. All the presented results for quasi-one-dimensional models of Schrödinger type include the case of Bernoulli randomness.
{\copyright 2023 American Institute of Physics}Quantum corrections to the entropy in a driven quantum Brownian motion modelhttps://zbmath.org/1521.820152023-11-13T18:48:18.785376Z"Qiu, Tian"https://zbmath.org/authors/?q=ai:qiu.tian"Quan, Hai-Tao"https://zbmath.org/authors/?q=ai:quan.hai-taoSummary: The quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. We obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy in the weak coupling limit. Moreover, we find that for the thermodynamic equilibrium initial state, all terms odd in \(\hbar\) are exactly zero. Our results bring important insights to the understanding of entropy in open quantum systems.Padé approximant approach to singular properties of quantum gases: the ideal caseshttps://zbmath.org/1521.820162023-11-13T18:48:18.785376Z"Tian, Yuan-Hong"https://zbmath.org/authors/?q=ai:tian.yuan-hong"Li, Wen-Du"https://zbmath.org/authors/?q=ai:li.wen-du"Shen, Yao"https://zbmath.org/authors/?q=ai:shen.yao"Dai, Wu-Sheng"https://zbmath.org/authors/?q=ai:dai.wushengSummary: In this paper, we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padé approximant. The virial expansion is a high-temperature and low-density expansion and in practice, often, only the first several virial coefficients can be obtained. For Bose gases, we determine the BEC phase transition from a truncated virial expansion. For Fermi gases, we recover the low-temperature and high-density result from the virial expansion.Erratum to: ``Thermodynamic uncertainty relations in a linear system''https://zbmath.org/1521.820172023-11-13T18:48:18.785376Z"Gupta, Deepak"https://zbmath.org/authors/?q=ai:gupta.deepak-kumar"Maritan, Amos"https://zbmath.org/authors/?q=ai:maritan.amosAn error in the first sentence in Section 3 of the authors' paper [ibid. 93, No. 2, Paper No. 28, 8 p. (2020; Zbl 1516.82066)] is corrected.A simplified Parisi ansatzhttps://zbmath.org/1521.820182023-11-13T18:48:18.785376Z"Franchini, Simone"https://zbmath.org/authors/?q=ai:franchini.simoneSummary: Based on simple combinatorial arguments, we formulate a generalized cavity method where the Random Overlap Structure (ROSt) probability space of Aizenmann, Sims and Starr is obtained in a constructive way, and we use it to give a simplified derivation of the Parisi formula for the free energy of the Sherrington-Kirkpatrick model.Eigen microstates and their evolutions in complex systemshttps://zbmath.org/1521.820192023-11-13T18:48:18.785376Z"Sun, Yu"https://zbmath.org/authors/?q=ai:sun.yu|sun.yu.5"Hu, Gaoke"https://zbmath.org/authors/?q=ai:hu.gaoke"Zhang, Yongwen"https://zbmath.org/authors/?q=ai:zhang.yongwen"Lu, Bo"https://zbmath.org/authors/?q=ai:lu.bo"Lu, Zhenghui"https://zbmath.org/authors/?q=ai:lu.zhenghui"Fan, Jingfang"https://zbmath.org/authors/?q=ai:fan.jingfang"Li, Xiaoteng"https://zbmath.org/authors/?q=ai:li.xiaoteng"Deng, Qimin"https://zbmath.org/authors/?q=ai:deng.qimin"Chen, Xiaosong"https://zbmath.org/authors/?q=ai:chen.xiaosongSummary: Emergence refers to the existence or formation of collective behaviors in complex systems. Here, we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of \(M\) microstates of a complex system with \(N\) agents is defined by the normalized \(N \times M\) matrix \(\boldsymbol{A}\), whose columns represent microstates and order of row is consist with the time. The ensemble matrix \(\boldsymbol{A}\) can be decomposed as \(\boldsymbol{A} = \sum_{I=1}^r\sigma_I\boldsymbol{U}_I\otimes\boldsymbol{V}_I\), where \(r = \min(N, M)\), eigenvalue \(\sigma_I\) behaves as the probability amplitude of the eigen microstate \(\boldsymbol{U}_I\) so that \(\sum_{I=1}^r\sigma_I^2=1\) and \(\boldsymbol{U}_I\) evolves following \(\boldsymbol{V}_I\). In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude \(\sigma_I\) becomes finite in the thermodynamic limit, there is a condensation of the eigen microstate \(\boldsymbol{U}_I\) in analogy to the Bose-Einstein condensation of Bose gases. This indicates the emergence of \(\boldsymbol{U}_I\) and a phase transition in complex system. Our framework has been applied successfully to equilibrium three-dimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown order-parameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.Edge effect and interface confinement modulated strain distribution and interface adhesion energy in graphene/Si systemhttps://zbmath.org/1521.820202023-11-13T18:48:18.785376Z"Huang, Ying-Di"https://zbmath.org/authors/?q=ai:huang.ying-di"Xie, Jia-Ting"https://zbmath.org/authors/?q=ai:xie.jia-ting"Hu, Su-Mei"https://zbmath.org/authors/?q=ai:hu.sumei"He, Yan"https://zbmath.org/authors/?q=ai:he.yan.1Summary: In order to clarify the edge and interface effect on the adhesion energy between graphene (Gr) and its substrate, a theoretical model is proposed to study the interaction and strain distribution of Gr/Si system in terms of continuum medium mechanics and nanothermodynamics. We find that the interface separation and adhesion energy are determined by the thickness of Gr and substrate. The disturbed interaction and redistributed strain in the Gr/Si system induced by the effect of surface and interface can make the interface adhesion energy decrease with increasing thickness of Gr and diminishing thickness of Si. Moreover, our results show that the smaller area of Gr is more likely to adhere to the substrate since the edge effect improves the active energy and strain energy. Our predictions can be expected to be a guide for designing high performance of Gr-based electronic devices.The relation between the radii and the densities of magnetic skyrmionshttps://zbmath.org/1521.820212023-11-13T18:48:18.785376Z"Bo, Yu-Jiao"https://zbmath.org/authors/?q=ai:bo.yu-jiao"Li, Wen-Wen"https://zbmath.org/authors/?q=ai:li.wenwen"Guo, Yu-Chen"https://zbmath.org/authors/?q=ai:guo.yuchen"Yang, Ji-Chong"https://zbmath.org/authors/?q=ai:yang.ji-chongSummary: Compared with the traditional magnetic bubble, a skyrmion has a smaller size, and better stability and therefore is considered as a very promising candidate for future memory devices. When skyrmions are manipulated, erased and created, the density of skyrmions can be varied, however the relationship between the radii and the densities of skyrmions needs more exploration. In this paper, we study this problem both theoretically and by using the lattice simulation. The average radius of skyrmions as a function of material parameters, the strength of the external magnetic field and the density of skyrmions is obtained and verified. With this explicit function, the skyrmion radius can be easily predicted, which is helpful for the future study of skyrmion memory devices.Superconducting gap ratio from strange metal phase in the absence of quasiparticleshttps://zbmath.org/1521.820222023-11-13T18:48:18.785376Z"Cai, Wenhe"https://zbmath.org/authors/?q=ai:cai.wenhe"Ge, Xian-Hui"https://zbmath.org/authors/?q=ai:ge.xianhuiSummary: A lattice model for strongly interacting electrons motivated by a rank-3 tensor model provides a tool for understanding the pairing mechanism of high-temperature superconductivity. This Sachdev-Ye-Kitaev-like model describes the strange metal phase in the cuprate high temperature superconductors. Our calculation indicates that the superconducting gap ratio in this model is higher than the ratio in the BCS theory due to the coupling term and the spin operator. Under certain conditions, the ratio also agrees with the BCS theory. Our results relate to the case of strong coupling, so it may pave the way to gaining insight into the cuprate high temperature superconductors.Grüneisen ratio quest for self-duality of quantum criticality in a spin-1/2 XY chain with Dzyaloshinskii-Moriya interactionhttps://zbmath.org/1521.820232023-11-13T18:48:18.785376Z"Ding, Lin-Jie"https://zbmath.org/authors/?q=ai:ding.lin-jie"Zhong, Yuan"https://zbmath.org/authors/?q=ai:zhong.yuanSummary: The quantum phase transition (QPT) and quantum criticality of an anisotropic spin-1/2 \(XY\) chain under the interplay of magnetic field and Dzyaloshinskii-Moriya (DM) interaction, which is interpreted as an electric field, are investigated, wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order. It is shown that the thermal Drude weight is a good quantity to characterize the gapped (\(D_{\mathrm{th}} = 0\)) and gapless (\(D_{\mathrm{th}} > 0\)) ground states. The continuous QPT is marked by a quantum critical point (QCP) associated with entropy accumulation, which is manifested by a characteristic Güneisen ratio (GR) with or without self-duality symmetry. It is shown that at a self-dual QCP, the GR keeps a finite value as \(T \rightarrow 0\), while at a general QCP without self-duality symmetry, it displays a power-law temperature dependent divergence: \(\Gamma (T, r_c) \sim \pm T^{-1}\), which provides a novel thermodynamic means for probing QPT.New holographic Weyl superconductors in Lifshitz gravityhttps://zbmath.org/1521.820242023-11-13T18:48:18.785376Z"Lu, Jun-Wang"https://zbmath.org/authors/?q=ai:lu.junwang"Wu, Ya-Bo"https://zbmath.org/authors/?q=ai:wu.yabo"Li, Huai-Fan"https://zbmath.org/authors/?q=ai:li.huaifan"Liao, Hao"https://zbmath.org/authors/?q=ai:liao.hao"Zheng, Yong"https://zbmath.org/authors/?q=ai:zheng.yong"Dong, Bao-Ping"https://zbmath.org/authors/?q=ai:dong.bao-pingSummary: We build holographic \(p\)-wave conductor(insulator)/superconductor models via the numerical method with a new form of Weyl coupling in five-dimensional Lifshitz gravity, and then investigate how the Weyl coupling parameter \(\gamma\) and the Lifshitz scaling parameter \(z\) affect the superconductor models. In the conductor/superconductor model, an increase in the Weyl correction (Lifshitz scaling) enhances (inhibits) the superconductor phase transition. Meanwhile, both the Weyl correction (when the Lifshitz parameter is large enough and fixed) and the Lifshitz scaling suppress the growth of the real part of the conductivity. The Weyl correction used here (\(CB^2\)) shows weaker effects on the critical value than the previous Weyl correction (\(CF^2\)). In the insulator/superconductor model, larger vaules of the Weyl parameter hinder the formation of condensate. However, in increase in the Lifshitz scaling enhances the appearance of condensate. In addition, the calculation suggests that a competitive relation may exist between the Weyl correction and the Lifshitz scaling.Role of four-spin exchange in a magnetic mechanism of superconductivity in cuprateshttps://zbmath.org/1521.820252023-11-13T18:48:18.785376Z"Shnurenko, Aleksandr V."https://zbmath.org/authors/?q=ai:shnurenko.aleksandr-v"Ovchinnikov, Sergeĭ G."https://zbmath.org/authors/?q=ai:ovchinnikov.sergei-g"Shneĭder, Elena I."https://zbmath.org/authors/?q=ai:shneider.elena-iSummary: Amendments to the exchange interaction can alter the superconducting transition temperature, so on the basis of numerical self-consistent solution of two equations in the framework of the \(t-J\) model, we investigate the influence of the four spin exchange on the concentration dependence of the transition temperature to the superconducting phase with \(d_{x^2-y^2}\) - the type of symmetry of the order.Vibrational features of graphene oxide powder nanocomposite coupled conical-cylindrical shells applicable for aerospace structures under various boundary conditionshttps://zbmath.org/1521.820262023-11-13T18:48:18.785376Z"Sobhani, Emad"https://zbmath.org/authors/?q=ai:sobhani.emad"Safaei, Babak"https://zbmath.org/authors/?q=ai:safaei.babak(no abstract)A neural network-based approach for bending analysis of strain gradient nanoplateshttps://zbmath.org/1521.820272023-11-13T18:48:18.785376Z"Yan, C. A."https://zbmath.org/authors/?q=ai:yan.c-a"Vescovini, R."https://zbmath.org/authors/?q=ai:vescovini.riccardo"Fantuzzi, N."https://zbmath.org/authors/?q=ai:fantuzzi.nicholas(no abstract)An efficient local RBF-based method for elasticity problems involving multiple material phaseshttps://zbmath.org/1521.820282023-11-13T18:48:18.785376Z"Gholampour, Faranak"https://zbmath.org/authors/?q=ai:gholampour.faranak"Hesameddini, Esmail"https://zbmath.org/authors/?q=ai:hesameddini.esmail"Taleei, Ameneh"https://zbmath.org/authors/?q=ai:taleei.ameneh(no abstract)Coupling molecular dynamics and direct simulation Monte Carlo using a general and high-performance code coupling libraryhttps://zbmath.org/1521.820292023-11-13T18:48:18.785376Z"Longshaw, S. M."https://zbmath.org/authors/?q=ai:longshaw.s-m"Pillai, R."https://zbmath.org/authors/?q=ai:pillai.raji-r|pillai.rohit|pillai.r-v-k|pillai.rekha|pillai.r-n"Gibelli, L."https://zbmath.org/authors/?q=ai:gibelli.livio"Emerson, D. R."https://zbmath.org/authors/?q=ai:emerson.david-r"Lockerby, D. A."https://zbmath.org/authors/?q=ai:lockerby.duncan-aSummary: A domain-decomposed method to simultaneously couple the classical Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC) methods is proposed. This approach utilises the MPI-based general coupling library, the Multiscale Universal Interface. The method provides a direct coupling strategy and utilises two OpenFOAM based solvers, mdFoam+ and dsmcFoam+, enabling scenarios where both solvers assume one discrete particle is equal to one molecule or atom. The ultimate goal of this work is to enable complex multi-scale simulations involving micro, meso and macroscopic elements, as found with problems like evaporation.
Results are presented to show the fundamental capabilities of the method in terms of mass and kinetic energy conservation between simulation regions handled by the different solvers. We demonstrate the capability of the method by deploying onto a large supercomputing resource, with attention paid to the scalability for a canonical NVT ensemble (a constant number of atoms \(N\), constant volume \(V\) and constant temperature \(T\)) of Argon atoms. The results show that the method performs as expected in terms of mass conservation and the solution is also shown to scale reasonably on a supercomputing resource, within the known performance limits of the coupled codes. The wider future of this work is also considered, with focus placed on the next steps to expand the capabilities of the methodology to allow for indirect coupling (where the coarse-graining capability of the DSMC method is used), as well as how this will then fit into a larger coupled framework to allow a complete micro-meso-macro approach to be tackled.Drug release using nanoparticles in the cancer cells on 2-D materials in order to target drug delivery: a numerical simulation via molecular dynamics methodhttps://zbmath.org/1521.820302023-11-13T18:48:18.785376Z"AlDosari, Sahar Mohammed"https://zbmath.org/authors/?q=ai:aldosari.sahar-mohammed"Banawas, Saeed"https://zbmath.org/authors/?q=ai:banawas.saeed"Ghafour, Hevi Seerwan"https://zbmath.org/authors/?q=ai:ghafour.hevi-seerwan"Tlili, Iskander"https://zbmath.org/authors/?q=ai:tlili.iskander"Quynh Hoang Le"https://zbmath.org/authors/?q=ai:quynh-hoang-le.(no abstract)Removal of formaldehyde pollutant from petroleum industry wastewaters by polymers: a molecular dynamics simulationhttps://zbmath.org/1521.820312023-11-13T18:48:18.785376Z"Henda, Mouna Ben"https://zbmath.org/authors/?q=ai:henda.mouna-ben"Sadon, Shayma Hamza"https://zbmath.org/authors/?q=ai:sadon.shayma-hamza"abdelmalek, Zahra"https://zbmath.org/authors/?q=ai:abdelmalek.zahra"Li, Zhixiong"https://zbmath.org/authors/?q=ai:li.zhixiong|li.zhixiong.1"Le, Quynh Hoang"https://zbmath.org/authors/?q=ai:le.quynh-hoang(no abstract)Molecular dynamics method for numerical study of thermal performance of hexacosane PCM in a Cu-nanochannelhttps://zbmath.org/1521.820322023-11-13T18:48:18.785376Z"Le, Quynh Hoang"https://zbmath.org/authors/?q=ai:le.quynh-hoang"Mohammad Sajadi, S."https://zbmath.org/authors/?q=ai:sajadi.s-mohammad"abdelmalek, Zahra"https://zbmath.org/authors/?q=ai:abdelmalek.zahra"Karooby, Elaheh"https://zbmath.org/authors/?q=ai:karooby.elaheh"Jamali Ghahderijani, Mehdi"https://zbmath.org/authors/?q=ai:jamali-ghahderijani.mehdi"Koochaki, Amin"https://zbmath.org/authors/?q=ai:koochaki.amin"Shahgholi, Mohamad"https://zbmath.org/authors/?q=ai:shahgholi.mohamad"Inc, Mustafa"https://zbmath.org/authors/?q=ai:inc.mustafa(no abstract)The molecular dynamics study of vacancy defect influence on carbon nanotube performance as drug delivery systemhttps://zbmath.org/1521.820332023-11-13T18:48:18.785376Z"Li, Shuai"https://zbmath.org/authors/?q=ai:li.shuai.1"Sajadi, S. Mohammad"https://zbmath.org/authors/?q=ai:sajadi.s-mohammad"Alharbi, Khalid Abdulkhaliq M."https://zbmath.org/authors/?q=ai:alharbi.khalid-abdulkhaliq-m"El-Shorbagy, M. A."https://zbmath.org/authors/?q=ai:el-shorbagy.mohammed-a"Tlili, Iskander"https://zbmath.org/authors/?q=ai:tlili.iskander(no abstract)Study of phase transition of Potts model with domain adversarial neural networkhttps://zbmath.org/1521.820342023-11-13T18:48:18.785376Z"Chen, Xiangna"https://zbmath.org/authors/?q=ai:chen.xiangna"Liu, Feiyi"https://zbmath.org/authors/?q=ai:liu.feiyi"Chen, Shiyang"https://zbmath.org/authors/?q=ai:chen.shiyang"Shen, Jianmin"https://zbmath.org/authors/?q=ai:shen.jianmin"Deng, Weibing"https://zbmath.org/authors/?q=ai:deng.weibing"Papp, Gábor"https://zbmath.org/authors/?q=ai:papp.gabor"Li, Wei"https://zbmath.org/authors/?q=ai:li.wei.16"Yang, Chunbin"https://zbmath.org/authors/?q=ai:yang.chunbinSummary: A transfer learning method, Domain Adversarial Neural Network (DANN), is introduced to study the phase transition of two-dimensional \(q\)-state Potts model. With the DANN, we only need to choose a few labeled configurations automatically as input data, then the critical points can be obtained after training the algorithm. By an additional iterative process, the critical points can be captured to comparable accuracy to Monte Carlo simulations as we demonstrate it for \(q = 3\), 4, 5, 7 and 10. The type of phase transition (first or second-order) is also determined at the same time. Meanwhile, for the second-order phase transition at \(q = 3\), we can calculate the critical exponent \(\nu\) by data collapse. Furthermore, compared to the traditional supervised learning, we found the DANN to be more accurate with lower cost.Relativistic liquids: GENERIC or EIT?https://zbmath.org/1521.830042023-11-13T18:48:18.785376Z"Gavassino, L."https://zbmath.org/authors/?q=ai:gavassino.lorenzo"Antonelli, M."https://zbmath.org/authors/?q=ai:antonelli.melissa|antonelli.michela|antonelli.miranda-j|antonelli.mattia|antonelli.michele|antonelli.massimo|antonelli.marcoSummary: We study the GENERIC hydrodynamic theory for relativistic liquids formulated by Öttinger and collaborators. We use the maximum entropy principle to derive its conditions for linear stability (in an arbitrary reference frame) and for relativistic causality. In addition, we show that, in the linear regime, its field equations can be recast into a symmetric-hyperbolic form. Once rewritten in this way, the linearised field equations turn out to be a particular realisation of the Israel-Stewart theory, where some of the Israel-Stewart free parameters are constrained. This also allows us to reinterpret the GENERIC framework in view of the principles of extended irreversible thermodynamics and to discuss its physical relevance to model (possibly viscoelastic) fluids.A guiding center implementation for relativistic particle dynamics in the PLUTO codehttps://zbmath.org/1521.830102023-11-13T18:48:18.785376Z"Mignone, A."https://zbmath.org/authors/?q=ai:mignone.andrea"Haudemand, H."https://zbmath.org/authors/?q=ai:haudemand.h"Puzzoni, E."https://zbmath.org/authors/?q=ai:puzzoni.eSummary: We present a numerical implementation of the guiding center approximation to describe the relativistic motion of charged test particles in the PLUTO code for astrophysical plasma dynamics. The guiding center approximation (GCA) removes the time step constraint due to particle gyration around magnetic field lines by following the particle center of motion rather than its full trajectory. The gyration can be detached from the guiding center motion if electromagnetic fields vary sufficiently slow compared to the particle gyration radius and period. Our implementation employs a variable step-size linear multistep method, more efficient when compared to traditional one-step Runge Kutta schemes. A number of numerical benchmarks is presented in order to assess the validity of our implementation.Gravitational waves and monopoles dark matter from first-order phase transitionhttps://zbmath.org/1521.830292023-11-13T18:48:18.785376Z"Yang, Jing"https://zbmath.org/authors/?q=au:Yang, Jing"Zhou, Ruiyu"https://zbmath.org/authors/?q=ai:zhou.ruiyu"Bian, Ligong"https://zbmath.org/authors/?q=ai:bian.ligongSummary: We study the possibility of monopoles serving as dark matter when they are produced during the first-order phase transition in the dark sector. Our study shows that dark monopoles can contribute only a small piece of dark matter relic density within parameter spaces where strong gravitational waves can be probed by ET and CE, and the monopoles can contribute a sizable component of the observed dark matter relic density for fast phase transitions with short duration.AdS to ds phase transition mediated by thermalon in Einstein-Gauss-Bonnet gravity from Rényi statisticshttps://zbmath.org/1521.830362023-11-13T18:48:18.785376Z"Samart, Daris"https://zbmath.org/authors/?q=ai:samart.daris"Channuie, Phongpichit"https://zbmath.org/authors/?q=ai:channuie.phongpichitSummary: In this work, we present the possible existence of a thermalon phase transition between anti-de Sitter (AdS) to de Sitter (dS) vacua in Einstein-Gauss-Bonnet gravity by considering the Rényi statistics. A thermalon changes the asymptotic structure of spacetimes via the bubble nucleation of spherical thin-shells which host a black hole in the interior. All relevant thermodynamical quantities are computed in terms of the Rényi statistics in order to demonstrate the possible existence of the AdS to dS phase transition. In addition, we also comment on the behaviors of the phase transitions in the Rényi statistics.Some remarks on relativistic fluids of divergence typehttps://zbmath.org/1521.830582023-11-13T18:48:18.785376Z"Salazar, J. Félix"https://zbmath.org/authors/?q=ai:salazar.j-felix"Zannias, Thomas"https://zbmath.org/authors/?q=ai:zannias.thomasSummary: Relativistic fluids of divergence type constitute a special class of fluids whose states are determined from the knowledge of a scalar generating function \(\chi\) and a dissipation tensor \(I^{\mu\nu}\) i.e. a second rank, symmetric and traceless tensor. Both \((\chi, I^{\mu\nu})\) depend upon fourteen variables, known in the literature as Lagrange multipliers, and these multipliers satisfy a symmetric, quasilinear, first order system determined by \((\chi, I^{\mu\nu})\). For particular choices of the generating function \(\chi\), this system can be symmetric-hyperbolic and causal. We show in this work that this characteristic property of fluids of divergence type originates in the overdetermined nature of their dynamical equations. Combining their overdetermined nature with the work of Friedrichs on overdetermined system of conservation laws with more recent work by Boillat, Ruggeri and coworkers, we prove that fluids of divergence type are locally determined by a vector potential depending upon the Lagrange multipliers. For the case where the dynamical variables describing fluid states contain a symmetric energy momentum tensor, this vector potential is the gradient of a scalar field and this field is precisely the generating function \(\chi\) introduced by Pennisi and independently by Geroch and Lindblom. Examples of scalar generating functions \(\chi\) are discussed where this system is a symmetric hyperbolic and causal system in an open vicinity of equilibrium states.Imaginary potential of heavy quarkonia from thermal fluctuations in rotating matter from holographyhttps://zbmath.org/1521.830752023-11-13T18:48:18.785376Z"Zhang, Zi-qiang"https://zbmath.org/authors/?q=ai:zhang.ziqiang"Zhu, Xiangrong"https://zbmath.org/authors/?q=ai:zhu.xiangrong"Hou, De-fu"https://zbmath.org/authors/?q=ai:hou.defuSummary: Using AdS/CFT correspondence, we study the imaginary part of heavy quarkonia potential from thermal fluctuations in a strongly coupled plasma. We perform the analysis in a rotating deformed AdS black-hole background. It is shown that the presence of angular velocity decreases the onset of imaginary potential thus enhancing quarkonia dissociation, in agreement with previous findings of the entropic force. Moreover, by increasing angular velocity, the thermal width becomes smaller.Extended phase space thermodynamics of black holes: a study in Einstein's gravity and beyondhttps://zbmath.org/1521.830902023-11-13T18:48:18.785376Z"Bhattacharya, Krishnakanta"https://zbmath.org/authors/?q=ai:bhattacharya.krishnakantaSummary: In the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in black holes has been found in modified theories of gravity as well, such as the \(f(R)\) gravity and the scalar-tensor gravity. However, in the case of these modified theories of gravity, the expression of pressure (and, hence, volume) is not uniquely determined. In addition, for these modified theories, the extended phase space thermodynamics has not been studied extensively, especially in a covariant way. Since both the scalar-tensor and the \(f(R)\) gravity can be discussed in the two conformally connected frames (the Jordan and the Einstein frame respectively), the arbitrariness in the expression of pressure, will act upon the equivalence of the thermodynamic parameters in the two frames. We highlight these issues in the paper. Before that, in Einstein's gravity (GR), we obtain a general expression of the equilibrium state version of first law and the Smarr-like formula from the Einstein's equation for a general static and spherically symmetric (SSS) metric. Unlike the existing formalisms in literature which defines thermodynamic potential in order to express the first law, here we directly obtain the first law as well as the Smarr-like formula in GR in terms of the parameters present in the metric (such as mass, charge \textit{etc.}). This study also shows how the extended phase space is formulated (by considering the cosmological constant as variable) and, also shows why the cosmological constant plays the role of thermodynamic pressure in GR in extended phase space. Moreover, obtaining the Smarr formula from the Einstein's equation for the SSS metric suggests that this dynamical equation encodes more information on BH thermodynamics than what has been anticipated before.Deflection angle evolution with plasma medium and without plasma medium in a parameterized black holehttps://zbmath.org/1521.831172023-11-13T18:48:18.785376Z"He, Xiaoling"https://zbmath.org/authors/?q=ai:he.xiaoling"Xu, Tianyu"https://zbmath.org/authors/?q=ai:xu.tianyu"Yu, Yun"https://zbmath.org/authors/?q=ai:yu.yun"Karamat, Anosha"https://zbmath.org/authors/?q=ai:karamat.anosha"Babar, Rimsha"https://zbmath.org/authors/?q=ai:babar.rimsha"Ali, Riasat"https://zbmath.org/authors/?q=ai:ali.riasatSummary: Using the Keeton and Petters approach, we determine the deflection angle. We also investigate the motion of photons around a parameterized black hole in the presence of non-magnetized cold plasma by using a new ray-tracing algorithm. In spherically symmetric spacetime, we examine the influence of the plasma by applying the Hamiltonian equation on the deflection angle as well as shadow. It is examine to derive the rays analytically from Hamilton's equation by separating the metric and the plasma frequency. We study that the presence of plasma affects the deflection angle as well as shadow for the parameterized black hole and they depend on plasma frequency. If the plasma frequency is significantly lower than the photon frequency, the photon sphere and shadow radius expressions can be linearized around the values found for space light rays. Furthermore, we have graphically analyze the behavior of shadow for distinct positions under the effects of plasma frequency as well as low density plasma medium.Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicleshttps://zbmath.org/1521.900442023-11-13T18:48:18.785376Z"Zhai, Cong"https://zbmath.org/authors/?q=ai:zhai.cong"Zhang, Ronghui"https://zbmath.org/authors/?q=ai:zhang.ronghui"Peng, Tao"https://zbmath.org/authors/?q=ai:peng.tao"Zong, Changfu"https://zbmath.org/authors/?q=ai:zong.changfu"Xu, Hongguo"https://zbmath.org/authors/?q=ai:xu.hongguo.2Summary: As communication and perception technologies develop, connected vehicles (CVs) advance rapidly. In the process of popularization of CVs, it is bound to lead to the coexistence of CVs and human-driven vehicles (HDVs) on the road network for some time to come, and the previous study assumes that road vehicle is homogeneous, which could not quantify the difference between mixed vehicular flow, based on this, we consider the differences between CAVs and CVs in the way of information acquisition, a heterogeneous lattice hydrodynamics model mixing the HDVs and CVs are presented. Subsequently, by using the small perturbation method, we analyze the linear stability of the proposed model and derive the corresponding stability criteria; when the above stability norm does not hold, in order to investigate the nonlinear phenomenon, nonlinear stability analysis is performed and a modified Korteweg-de Vries equation (mKdV) corresponding to the proposed model is derived. By solving the mKdV equation, we obtain the kink-antikink solitary wave solution which can be used to explain how traffic jams form and propagate. At last, several numerical simulations were conducted to test the impact of the penetration rate of CVs and the bi-directional visual field for both forward-looking and backward-looking on the heterogeneous traffic flow stability, i.e., the first two are positive, while the last is negligible, this conclusion is consistent with the conclusion of theoretical derivation.Corrigendum to: ``Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles''https://zbmath.org/1521.900452023-11-13T18:48:18.785376Z"Zhai, Cong"https://zbmath.org/authors/?q=ai:zhai.cong"Zhang, Ronghui"https://zbmath.org/authors/?q=ai:zhang.ronghui"Peng, Tao"https://zbmath.org/authors/?q=ai:peng.tao"Zong, Changfu"https://zbmath.org/authors/?q=ai:zong.changfu"Xu, Hongguo"https://zbmath.org/authors/?q=ai:xu.hongguo.2From the text: The fourth author's name in [ibid. 623, Article ID 128903, 18 p. (2023; Zbl 1521.90044)] is corrected.Influences of flexible defect on the interplay of supercoiling and knotting of circular DNAhttps://zbmath.org/1521.920662023-11-13T18:48:18.785376Z"Xiong, Caiyun"https://zbmath.org/authors/?q=ai:xiong.caiyun"Nie, Xiaolin"https://zbmath.org/authors/?q=ai:nie.xiaolin"Peng, Yixue"https://zbmath.org/authors/?q=ai:peng.yixue"Zhou, Xun"https://zbmath.org/authors/?q=ai:zhou.xun"Fan, Yangtao"https://zbmath.org/authors/?q=ai:fan.yangtao"Chen, Hu"https://zbmath.org/authors/?q=ai:chen.hu|chen.hu.1"Liu, Yanhui"https://zbmath.org/authors/?q=ai:liu.yanhuiSummary: Knots are discovered in biophysical systems, such as DNA and proteins. Knotted portions in knotted DNA are significantly bent and their corresponding bending angles are comparable with or larger than the sharp bending angle resulting in flexible defects. The role of flexible defects in the interplay of supercoiling and knotting of circular DNA were predicted by a Monte Carlo simulation. In knotted DNA with a particular knot type, a flexible defect noticeably enhances the supercoiling of the knotted DNA and the decreasing excitation energy makes the knotted portion more compact. A reduction in twist rigidity and unwinding of flexible defects are incorporated into the numerical simulations, so that interplay of supercoiling and knotting of circular DNA is studied under torsional conditions. Increasing unwinding not only results in a wider linking number distribution, but also leads to a drift of the distribution to lower values. A flexible defect has obvious effects on knotting probability. The summation of equilibrium distribution probability for nontrivial knotted DNA with different contour length does not change with excitation energy monotonically and has a maximum at an intermediate value of excitation energy around \(5k_BT\). In the phase space of knot length and gyration radius of knotted DNA, knot length does not anticorrelate with its gyration radius, which is attributed to the flexible defect in the knotted portion, which leads to the release of bending energy and inhibited the competition between entropy and bending energy.