Journal of Statistical Physics最新文献

{"title":"Macroscopic Thermalization for Highly Degenerate Hamiltonians After Slight Perturbation","authors":"Barbara Roos,&nbsp;Shoki Sugimoto,&nbsp;Stefan Teufel,&nbsp;Roderich Tumulka,&nbsp;Cornelia Vogel","doi":"10.1007/s10955-025-03493-y","DOIUrl":"10.1007/s10955-025-03493-y","url":null,"abstract":"<div><p>We say of an isolated macroscopic quantum system in a pure state <span>(psi )</span> that it is in macroscopic thermal equilibrium (MATE) if <span>(psi )</span> lies in or close to a suitable subspace <span>(mathcal {H}_textrm{eq})</span> of Hilbert space. It is known that every initial state <span>(psi _0)</span> will eventually reach and stay there most of the time (“thermalize”) if the Hamiltonian is non-degenerate and satisfies the appropriate version of the eigenstate thermalization hypothesis (ETH), i.e., that every eigenvector is in MATE. Tasaki recently proved the ETH for a certain perturbation <span>(H_theta ^textrm{fF})</span> of the Hamiltonian <span>(H_0^textrm{fF})</span> of <span>(Ngg 1)</span> free fermions on a one-dimensional lattice. The perturbation is needed to remove the high degeneracies of <span>(H_0^textrm{fF})</span>. Here, we first point out that also for degenerate Hamiltonians all <span>(psi _0)</span> thermalize if the ETH holds, i.e., if <i>every</i> eigenbasis lies in MATE, and we prove that this is the case for <span>(H_0^textrm{fF})</span>. Inspired by the fact that there is <i>one</i> eigenbasis of <span>(H_0^textrm{fF})</span> for which MATE can be proved more easily than for the others, with smaller error bounds, and also in higher spatial dimensions, we show for any given <span>(H_0)</span> that the existence of one eigenbasis in MATE implies quite generally that <i>most</i> eigenbases of <span>(H_0)</span> lie in MATE. We also show that, as a consequence, after adding a small generic perturbation, <span>(H=H_0+lambda V)</span> with <span>(lambda ll 1)</span>, for most perturbations <i>V</i> the perturbed Hamiltonian <i>H</i> satisfies ETH and all states thermalize.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12296827/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144726386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generating Function for Quantum Depletion of Bose-Einstein Condensates","authors":"Simone Rademacher","doi":"10.1007/s10955-025-03495-w","DOIUrl":"10.1007/s10955-025-03495-w","url":null,"abstract":"<div><p>We consider a Bose gas on the unit torus at zero temperature in the Gross-Pitaevskii regime, known to perform Bose-Einstein condensation: a macroscopic fraction of the bosons occupy the same quantum state, called condensate. We study the Bose gas’ quantum depletion, that is the number of bosons outside the condensate, and derive an explicit asymptotic formula of its generating function. Moreover, we prove an upper bound for the tails of the quantum depletion.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12296785/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144726385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mesoscopic and Macroscopic Entropy Balance Equations in a Stochastic Dynamics and Its Deterministic Limit","authors":"Hong Qian,&nbsp;Zhongwei Shen","doi":"10.1007/s10955-025-03489-8","DOIUrl":"10.1007/s10955-025-03489-8","url":null,"abstract":"<div><p>Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or a deterministic dynamics exhibiting chaotic behaviors. By taking the former approach based on the general diffusion process with diffusion <span>(alpha ^{-1}varvec{D}(textbf{x}))</span> and drift <span>(textbf{b}(textbf{x}))</span>, where <span>(alpha )</span> represents the “size parameter” of a system, we show that there are two distinctly different entropy balance equations. One reads <span>(textrm{d}S^{(alpha )}/textrm{d}t = e^{(alpha )}_p + Q^{(alpha )}_{ex})</span> for all <span>(alpha )</span>. Our key result addresses the asymptotic of the entropy production rate <span>(e^{(alpha )}_p)</span> and heat exchange rate <span>(Q^{(alpha )}_{ex})</span> up to <span>(O(tfrac{1}{alpha }))</span>-corrections as system’s size <span>(alpha rightarrow infty )</span>. It yields in particular that the “extensive”, leading <span>(alpha )</span>-order terms of <span>(e^{(alpha )}_p)</span> and <span>(Q^{(alpha )}_{ex})</span> are exactly canceled out. Therefore in the asymptotic limit of <span>(alpha rightarrow infty )</span>, there is a second, local entropy balance equation <span>(textrm{d}S/textrm{d}t=nabla cdot textbf{b}(textbf{x}(t))+left( varvec{D}:varvec{varSigma }^{-1}right) (textbf{x}(t)))</span> on the order of <i>O</i>(1), where <span>(alpha ^{-1}varvec{D}(textbf{x}(t)))</span> represents the randomness generated in the dynamics usually represented by metric entropy, <span>(alpha ^{-1}varvec{varSigma }(textbf{x}(t)))</span> is the covariance matrix of the local Gaussian description at <span>(textbf{x}(t))</span> that is a solution to the ordinary differential equation <span>(dot{textbf{x}}=textbf{b}(textbf{x}))</span> at time <i>t</i>, and <span>(varvec{D}:varvec{varSigma }^{-1})</span> is the Frobenius product of <span>(varvec{D})</span> and <span>(varvec{varSigma }^{-1})</span>. This latter equation is akin to the notions of volume-preserving conservative dynamics and entropy production in the deterministic dynamic approach to irreversible thermodynamics <i>à la</i> D. Ruelle [55]. Our study follows the rigorous approach and formalism of [28]; the mathematical details with sufficient care are given in the appendices.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Some Random Billiards in a Tube with Superdiffusion","authors":"Henk Bruin,&nbsp;Niels Kolenbrander,&nbsp;Dalia Terhesiu","doi":"10.1007/s10955-025-03490-1","DOIUrl":"10.1007/s10955-025-03490-1","url":null,"abstract":"<div><p>We consider a class of random billiards in a tube, where reflection angles at collisions with the boundary of the tube are random variables rather than deterministic (and elastic) quantities. We obtain a (non-standard) Central Limit Theorem for the displacement of a particle, which marginally fails to have a second moment w.r.t. the invariant measure of the random billiard.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03490-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the First Positive Position of a Random Walker","authors":"Claude Godrèche,&nbsp;Jean-Marc Luck","doi":"10.1007/s10955-025-03491-0","DOIUrl":"10.1007/s10955-025-03491-0","url":null,"abstract":"<div><p>The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of this distribution, focusing particularly on its moments and asymptotic tail behaviour, in the case where the step distribution is continuous and symmetric, encompassing both diffusive random walks and Lévy flights.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Brownian Motion in the ({varvec{p}}) -Adic Integers is a Limit of Discrete Time Random Walks","authors":"Tyler Pierce,&nbsp;David Weisbart","doi":"10.1007/s10955-025-03474-1","DOIUrl":"10.1007/s10955-025-03474-1","url":null,"abstract":"<div><p>Vladimirov defined an operator on balls in <span>(mathbb {Q}_{p})</span>, the <i>p</i>-adic numbers, analogous to the Laplace operator in the real setting. Kochubei later gave a probabilistic interpretation of this operator. The Vladimirov–Kochubei operator generates a real-time diffusion process in the ring of <i>p</i>-adic integers, a Brownian motion in <span>(mathbb {Z}_{p})</span>. The current work proves that this process is a limit of discrete-time random walks. It motivates the construction of the Vladimirov–Kochubei operator, provides further intuition about ultrametric diffusion, and gives an example of the weak convergence of stochastic processes in a profinite group.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03474-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Existence and Sharp Decay Estimates of Classical Solutions to the Vlasov-Poisson System with Radiation Damping","authors":"Fucai Li,&nbsp;Man Wu","doi":"10.1007/s10955-025-03484-z","DOIUrl":"10.1007/s10955-025-03484-z","url":null,"abstract":"<div><p>In this paper we consider the two-species Vlasov-Poisson system with a radiation damping term <span>(D^{[3]}(t))</span> in the whole space <span>(mathbb {R}^3)</span>, which was introduced by Bauer [Kinet. Relat. Models 11 (2018), 25–42] to approximate the relativistic Vlasov-Maxwell system, a fundamental model of dynamics of collisionless plasma. We obtain the global existence of solutions and optimal pointwise decay estimates of the charge densities and the electrostatic potential to this system for small initial data without any compact support assumptions. To prove our results, we mainly use the modified vector field method and a bootstrap method. There are two main novelties in our arguments: we introduce new modified functions of modified vector fields to control the troublesome terms involving <span>(D^{[3]}(t))</span> since it leads to loss an order derivative, and we raise a new bootstrap assumption and carry out new bootstrap arguments.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extensions of the Brascamp-Lieb Inequality and the Dipole Gas","authors":"Joseph G. Conlon,&nbsp;Michael Dabkowski","doi":"10.1007/s10955-025-03478-x","DOIUrl":"10.1007/s10955-025-03478-x","url":null,"abstract":"<div><p>This paper is concerned with <span>(dge 2)</span> lattice field models with action <span>(V(nabla phi (cdot )))</span>, where <span>(V:mathbb {R}^drightarrow mathbb {R})</span> is a uniformly convex function. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03478-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Identification of Key Propagation Nodes in Complex Networks Based on Weighted Multi-Feature Fusion and Approximate Influence Radius","authors":"Haoming Guo,&nbsp;Xuefeng Yan,&nbsp;Juping Zhang","doi":"10.1007/s10955-025-03482-1","DOIUrl":"10.1007/s10955-025-03482-1","url":null,"abstract":"<div><p>Identifying key propagation nodes in complex networks is an important research topic. We propose a new gravity model based on weighted multi-feature fusion and approximate influence radius (WMGM) to identify key propagation nodes. The core of this method is to first determine the approximate influence radius of nodes based on node similarity and network structure. Secondly, the normalized maximum eigenvector was introduced, and the element value of the eigenvector was regarded as the node weight value. Then, the K-shell value, degree value, and PageRank centrality of the node are fused, and the fused value is used as the mass of the node. Finally, based on the multi-feature fusion gravity model with weight attribute, the interaction force between nodes was calculated, and the importance score of nodes was determined by accumulating the interaction force of all nodes within the approximate influence radius. The WMGM method is compared with the classical centrality methods, the similar methods, and the state-of-the-art methods on 10 different real datasets. The experimental results show that the WMGM method can effectively identify the top 10 critical nodes in different networks, and the top 200 identified nodes are highly similar to the standard ranking results. In addition, the WMGM achieves high node ranking accuracy across all 10 datasets, attaining the best overall performance on 80% of them.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ergodic Optimization for Continuous Functions on the Dyck-Motzkin Shifts","authors":"Mao Shinoda,&nbsp;Hiroki Takahasi,&nbsp;Kenichiro Yamamoto","doi":"10.1007/s10955-025-03486-x","DOIUrl":"10.1007/s10955-025-03486-x","url":null,"abstract":"<div><p>Ergodic optimization aims to describe properties of invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet with non-unique maximal entropy measures. We show that the space of continuous functions on any Dyck-Motzkin shift contains two disjoint subsets: one is a dense <span>(G_delta )</span> set with empty interior for which any maximizing measure is not mixing and has zero entropy; the other is a dense set of functions for which there exist uncountably many, fully supported maximizing measures that are Bernoulli. Key ingredients of a proof of this result are the density of closed orbit measures in the space of ergodic measures and the path connectedness of the space of ergodic measures of any Dyck-Motzkin shift.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}