Journal of Statistical Physics最新文献

{"title":"Absence of Nontrivial Local Conserved Quantities in the Hubbard Model on the Two or Higher Dimensional Hypercubic Lattice","authors":"Mahiro Futami","doi":"10.1007/s10955-026-03665-4","DOIUrl":"10.1007/s10955-026-03665-4","url":null,"abstract":"<div><p>By extending the strategy developed by Shiraishi in 2019, we prove that the standard Hubbard model on the <i>d</i>-dimensional hypercubic lattice with <span>(dge 2)</span> does not admit any nontrivial local conserved quantities. The theorem strongly suggests that the model is non-integrable. To our knowledge, this is the first extension of Shiraishi’s proof of the absence of conserved quantities to a fermionic model. Although our proof follows the original strategy of Shiraishi, it is essentially more subtle compared with the proof by Shiraishi and Tasaki of the corresponding theorem for <span>(S=tfrac{1}{2})</span> quantum spin systems in two or higher dimensions. The difficulty comes mainly from the fact that both the one-dimensional Hubbard model and the model with <span>(U=0)</span> (i.e., the free fermion) in any dimension are integrable.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614737","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":"Exact Rheology of Uniform Shear Flow in a Gas of Inelastic and Rough Maxwell Particles","authors":"Andrés Santos,&nbsp;Gilberto M. Kremer","doi":"10.1007/s10955-026-03675-2","DOIUrl":"10.1007/s10955-026-03675-2","url":null,"abstract":"<div><p>We investigate the steady uniform shear flow of a granular gas composed of inelastic and rough Maxwell particles. Exploiting the mean-field character of the model, we derive exact expressions for the collisional production rates of the second-degree moments and obtain a closed nonlinear solution for the stress and spin-spin tensors. The rotational-to-translational temperature ratio and the proportionality between the spin-spin and stress tensors are shown to be independent of the coefficient of normal restitution and determined solely by roughness and moment of inertia. The reduced normal stresses, shear stress, and shear rate are obtained explicitly in terms of two effective parameters generalizing the cooling and stress relaxation rates of the smooth model. From these results we derive exact expressions for the non-Newtonian shear viscosity, the first viscometric function, and the friction coefficient. The dependence of the rheological properties on the normal and tangential restitution coefficients is analyzed in detail, revealing strong non-Newtonian behavior and nonmonotonic effects of roughness. The results reduce, in the appropriate limits, to those of the inelastic Maxwell model for smooth particles and to the Pidduck gas in the elastic perfectly rough case.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03675-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628588","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":"Nonlinear Projection for Ballistic Correlation Functions: a Formula in Terms of Minimal Connected Covers","authors":"Benjamin Doyon","doi":"10.1007/s10955-026-03659-2","DOIUrl":"10.1007/s10955-026-03659-2","url":null,"abstract":"<div><p>In many-body systems, the dynamics is governed, at large scales of space and time, by the hydrodynamic principle of projection onto the conserved densities admitted by the model. This is formalised as local relaxation of fluctuations in the Ballistic Macroscopic Fluctuation Theory, and is a nonlinear version of the Boltzmann-Gibbs principle. We use it to derive a projection formula, expressing <i>n</i>-point connected correlation functions (cumulants) of local observables at different space-time points, in terms of those of conserved densities. This applies in every <span>(dge 1)</span> spatial dimensions and under the ballistic scaling of space and time, both in and out of equilibrium. It generalises the well-known linear-response principle for 2-point functions. For higher-point functions, one needs to account for nonlinear fluctuations of conserved densities and, correspondingly, higher derivatives of local averages. Using Malyshev’s formula for the cumulant expansion, and keeping the leading order, the result is a nonlinear projection, expressed as a sum of products of correlation functions of conserved densities with equilibrium multivariances as coefficients. The sum is combinatorially organised via certain covers of the set of space-time points, which we call “minimal connected covers”. We use this in order to get general, explicit formulas for two- and three-point functions in stationary states, expressed in terms of thermodynamic and Euler-scale data.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03659-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614802","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":"Multi-floor Generalization of TASEP","authors":"Yuliy Baryshnikov,&nbsp;Alexander L. Stolyar","doi":"10.1007/s10955-026-03671-6","DOIUrl":"10.1007/s10955-026-03671-6","url":null,"abstract":"<div><p>We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed by a <i>back-pressure</i> (BP) algorithm (also often called <i>MaxWeight</i>). There are <i>N</i> sites (with <i>N</i> finite or infinite), each may contain at most <i>c</i> particles, <span>(1 le c &lt; infty )</span>. New particles enter the system at the left-most site 1 as a Poisson process of rate <span>(alpha le 1)</span>, unless site 1 has <i>c</i> particles. Particles (if any) are removed from the right-most site <i>N</i> as a Poisson process of rate <span>(beta le 1)</span>. The left-to-right movement of particles between neighboring sites is governed by the BP rule: one particle moves from site <i>n</i> to <span>(n+1)</span> at epochs of a rate 1 Poisson process, as long as the former site has strictly more particles than the latter. When <span>(c=1)</span>, this is the standard TASEP. Our main results address the asymptotics of the stationary distribution of a finite system, and especially the limit of the flux (current) as <span>(Nrightarrow infty )</span>. In particular, we prove that interesting non-trivial phase transitions take place in a system with <span>(c&gt;1)</span>. For example, if <span>(c&gt;1)</span> and <span>(1/2 le beta le 1)</span>, the maximum limiting flux 1/4 is achieved as long as <span>(alpha ge alpha _c^*)</span>, where <span>(alpha _c^* &lt; 1/2)</span> is some non-trivial threshold. (For the standard TASEP the threshold is 1/2.) We also put forward a general conjecture about the stationary distribution asymptotics under an arbitrary parameter setting. We illustrate our formal results and the conjecture by simulations, and identify interesting directions for further research.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03671-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614759","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":"Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distribution","authors":"Ivan Dornic,&nbsp;Robert Conte","doi":"10.1007/s10955-026-03608-z","DOIUrl":"10.1007/s10955-026-03608-z","url":null,"abstract":"<div><p>We determine the full persistence probability distribution for a non-Markovian stochastic process, motivated by first-passage questions arising in interacting spin systems and allied systems. We show that this distribution is governed by a distinguished Painlevé VI system arising from an exact Fredholm Pfaffian structure associated with the integrable <i>sech</i> kernel, <span>(K_{textrm{sech}}=1/(2 pi cosh [(x-y)/2]))</span>. The universal persistence exponent originally obtained by Derrida, Hakim and Pasquier is recovered as an asymptotic observable and acquires a natural geometric interpretation. In the stationary scaling regime, the persistence probability admits an exact Pfaffian decomposition into even and odd Fredholm determinants of the integrable sech kernel. These determinants are controlled by a unique global solution of a second-order nonlinear ordinary differential equation, which is identified as a particular Painlevé VI equation. The corresponding Painlevé VI connection problem determines the persistence exponent as a limiting value at infinity. We further show that the Painlevé VI system governing persistence admits a direct geometric interpretation: the relevant solution coincides with the mean curvature of a one-parameter family of Bonnet surfaces immersed in <span>(mathbb R^3)</span>. A folding transformation between such surfaces singles out the Painlevé VI equation with Manin coefficients [0, 0, 0, 0], which in particular governs the universal persistence distribution in the symmetric Ising case. In this framework, the persistence exponent is identified with the asymptotic mean curvature of the associated surface.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03608-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614388","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":"Boundary-driven quantum systems near the Zeno limit: steady states and long-time behavior","authors":"Eric A. Carlen,&nbsp;David A. Huse,&nbsp;Joel L. Lebowitz","doi":"10.1007/s10955-026-03664-5","DOIUrl":"10.1007/s10955-026-03664-5","url":null,"abstract":"&lt;div&gt;&lt;p&gt;We study composite open quantum systems with a finite-dimensional state space &lt;span&gt;(mathcal {H}_{AB} = mathcal {H}_Aotimes mathcal {H}_B)&lt;/span&gt; governed by a Lindblad equation &lt;span&gt;(displaystyle {frac{textrm{d}}{textrm{d}t}rho (t) = mathcal {L}_gamma rho (t)})&lt;/span&gt; where &lt;span&gt;(mathcal {L}_gamma rho = -i[H,rho ] + gamma mathcal {D}rho )&lt;/span&gt;. Here, &lt;i&gt;H&lt;/i&gt; is a Hamiltonian on &lt;span&gt;(mathcal {H}_{AB})&lt;/span&gt; while &lt;span&gt;(mathcal {D})&lt;/span&gt; is a dissipator &lt;span&gt;(mathcal {D}_Aotimes mathbbm {1})&lt;/span&gt; acting non-trivially only on part &lt;i&gt;A&lt;/i&gt; of the system, which can be thought of as the boundary, and &lt;span&gt;(gamma )&lt;/span&gt; is a parameter. It is known that the dynamics may simplify as the Zeno limit, &lt;span&gt;(gamma rightarrow infty )&lt;/span&gt;, is approached, so that after a initial time of order &lt;span&gt;(gamma ^{-1})&lt;/span&gt;, &lt;span&gt;(rho (t))&lt;/span&gt; is well approximated by &lt;span&gt;(pi _Aotimes R(t))&lt;/span&gt; where &lt;span&gt;(pi _A)&lt;/span&gt; is a density matrix on &lt;span&gt;(mathcal {H}_A)&lt;/span&gt; such that &lt;span&gt;(mathcal {D}_Api _A =0)&lt;/span&gt;, and &lt;i&gt;R&lt;/i&gt;(&lt;i&gt;t&lt;/i&gt;) is an approximate solution of &lt;span&gt;({displaystyle frac{textrm{d}}{textrm{d}t}R(t) = mathcal {L}_{P,gamma }R(t)})&lt;/span&gt; where &lt;span&gt;(mathcal {L}_{P,gamma } R:= -i[H_P,R] + gamma ^{-1} mathcal {D}_P R)&lt;/span&gt; with &lt;span&gt;(H_P)&lt;/span&gt; being a Hamiltonian on &lt;span&gt;(mathcal {H}_B)&lt;/span&gt; and &lt;span&gt;(mathcal {D}_P)&lt;/span&gt; being a Lindblad generator acting on density matrices on &lt;span&gt;(mathcal {H}_B)&lt;/span&gt;. We give a rigorous proof of this holding in greater generality than in previous work; we assume only that &lt;span&gt;(mathcal {D}_A)&lt;/span&gt; is ergodic and gapped. Moreover, we precisely control the error terms, and use this to show that the mixing times of &lt;span&gt;(mathcal {L}_gamma )&lt;/span&gt; and &lt;span&gt;(mathcal {L}_{P,gamma })&lt;/span&gt; are tightly related near the Zeno limit. Despite this connection, the errors in the approximate description of the evolution accumulate on times of order &lt;span&gt;(gamma ^2)&lt;/span&gt;, so it is difficult to directly access steady states &lt;span&gt;(bar{rho }_gamma )&lt;/span&gt; of &lt;span&gt;(mathcal {L}_gamma )&lt;/span&gt; through study of &lt;span&gt;(mathcal {L}_{P,gamma })&lt;/span&gt;. In order to better control the long time behavior, and in particular the steady states &lt;span&gt;(bar{rho }_gamma )&lt;/span&gt;, we introduce a third Lindblad generator &lt;span&gt;(mathcal {D}_P^sharp )&lt;/span&gt; that does not involve &lt;span&gt;(gamma )&lt;/span&gt;, but is still closely related to &lt;span&gt;(mathcal {L}_gamma )&lt;/span&gt; and &lt;span&gt;(mathcal {L}_{P,gamma })&lt;/span&gt;. We show that if &lt;span&gt;(mathcal {D}_P^sharp )&lt;/span&gt; is ergodic and gapped, then so are &lt;span&gt;(mathcal {L}_gamma )&lt;/span&gt; and &lt;span&gt;(mathcal {L}_{P,gamma })&lt;/span&gt; for all large &lt;span&gt;(gamma )&lt;/span&gt;, and in this case, if &lt;span&gt;(bar{rho }_gamma )&lt;/span&gt; denotes the unique steady state for &lt;span&gt;(mathcal {L}_gamma )&lt;/span&gt;, then &lt;span&gt;(lim _{gamma rightarrow infty }bar{rho }_gamma = pi _Aotimes bar{R})&lt;/span&gt; where &lt;span&gt;(bar{R})&lt;/span&gt; is the unique steady state for &lt;span&gt;(mathcal ","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03664-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614574","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":"First Order Non-Instantaneous Corrections in Collisional Kinetic Alignment Models","authors":"Laura Kanzler,&nbsp;Carmela Moschella,&nbsp;Christian Schmeiser","doi":"10.1007/s10955-026-03654-7","DOIUrl":"10.1007/s10955-026-03654-7","url":null,"abstract":"<div><p>In this work the standard kinetic theory assumption of instantaneous collisions is lifted. A model for higher order non-instantaneous alignment collisions is presented and studied in the asymptotic regime of short collision duration. A first order accurate approximative model is derived as a correction to the instantaneous limit. Rigorous results on its well-posedness and on the instantaneous limit are proven. The approximative model is a system of two equations. An equally accurate scalar approximation is suggested.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13400583/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148590086","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":"Mean-Field Limit for Singular Potentials in Non-Convex Domains with Reflection","authors":"Yeqing Shan,&nbsp;Guangying Lv","doi":"10.1007/s10955-026-03662-7","DOIUrl":"10.1007/s10955-026-03662-7","url":null,"abstract":"<div><p>The mean-field limit of interacting particle systems with singular interaction potentials under reflecting boundary conditions in non-convex domains is considered. To rigorously connect the microscopic particle system with its mesoscopic counterpart, we construct the empirical measure and establish stability by means of weighted exponential functionals. The main technical difficulties arise from the combination of non-convex geometry and singular particle interactions. To overcome the latter, we employ a smoothing (mollification) procedure of the interaction kernel, and then pass to the singular limit. For the boundary contribution, we exploit the exact shape of the boundary to keep the reflection terms under control. By combining moment bounds, stopping-time arguments, and mean-square error estimates for the empirical measure, we prove propagation of chaos and convergence to the reflected McKean-Vlasov equation.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614068","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":"Spectra as a classical phenomenon, and the Einstein classical program","authors":"Andrea Carati,&nbsp;Luigi Galgani,&nbsp;Fabrizio Gangemi","doi":"10.1007/s10955-026-03668-1","DOIUrl":"10.1007/s10955-026-03668-1","url":null,"abstract":"<div><p>According to Born (<i>Atomic Physics, page 103</i>), spectra are <i>“quantum phenomena, which from a classical standpoint are perfectly unintelligible”</i>. However we illustrate results on classical calculations of infrared spectra of ionic crystals (actually LiF) which show that the situation is much more complex. Indeed it turns out that: 1) At room temperature and at higher ones (up to 1060 K) the classical computations reproduce the experimental data, even better than the <i>presently available</i> quantum ones do; 2) At lower temperatures (even at 7.5 K), the classical computations reproduce pretty well the data, if one accepts the idea advanced in 1916 by Nernst (the inventor of the third principle) that zero-point energy has room in classical physics too. It is eventually pointed out that the mentioned results might be regarded as a first step towards an implementation of the Einstein Classical Program, which aims at deducing quantum physics (admittedly the correct theory) from a realistic theory. In fact, we are considering the Einstein classical program in the extreme version in which the realistic theory is just (<i>essentially, see below</i>) classical electrodynamics of matter in bulk, involving phase space orbits, solutions of Newton equations. An Appendix is devoted to illustrate the Nernst approach, which concerns also the relation between equipartition and Planck’s law.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03668-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613909","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":"Free Convolution and Generalized Dyson Brownian Motion","authors":"Pierre Bousseyroux,&nbsp;Jean-Philippe Bouchaud","doi":"10.1007/s10955-026-03641-y","DOIUrl":"10.1007/s10955-026-03641-y","url":null,"abstract":"<div><p>The eigenvalue spectrum of the sum of large random matrices that are mutually “free”, i.e., randomly rotated, can be obtained using the formalism of <i>R</i>-transforms, with many applications in different fields. We provide a direct interpretation of the otherwise abstract additivity property of <i>R</i>-transforms for the sum in terms of a dynamical evolution of “particles” (the eigenvalues), interacting through two-body and higher-body forces and subject to a Gaussian noise, generalizing the usual Dyson Brownian motion with Coulomb interaction. Interestingly, the appearance of an outlier outside of the bulk of the spectrum is signalled by a divergence of the “velocity” of the generalized Dyson motion. We also investigate the evolution of eigenvectors, extend our results to products of free matrices, and study the singular values of a non-Hermitian matrix perturbed by a bi-invariant random matrix.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613513","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}