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Existence and Uniqueness of Nonsimple Multiple SLE 非简单多重 SLE 的存在性和唯一性
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-08-11 DOI: 10.1007/s10955-024-03306-8
Dapeng Zhan
{"title":"Existence and Uniqueness of Nonsimple Multiple SLE","authors":"Dapeng Zhan","doi":"10.1007/s10955-024-03306-8","DOIUrl":"https://doi.org/10.1007/s10955-024-03306-8","url":null,"abstract":"<p>We prove the existence and uniqueness of multiple <span>(hbox {SLE}_{kappa })</span> associated with any given link pattern for <span>(kappa in (4,6])</span>. We also have the uniqueness for <span>(kappa in (6,8))</span>. The multiple <span>(hbox {SLE}_{kappa })</span> law is constructed by first inductively constructing a <span>(sigma )</span>-finite multiple <span>(hbox {SLE}_{kappa })</span> measure and then normalizing the measure whenever it is finite. The total mass of the measure satisfies the conformal covariance, asymptotics and PDE for multiple <span>(hbox {SLE}_{kappa })</span> partition functions in the literature subject to the assumption that it is smooth.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940092","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}
引用次数: 0
Prethermalization and Conservation Laws in Quasi-Periodically Driven Quantum Systems 准周期驱动量子系统中的预热和守恒定律
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-08-10 DOI: 10.1007/s10955-024-03313-9
Matteo Gallone, Beatrice Langella
{"title":"Prethermalization and Conservation Laws in Quasi-Periodically Driven Quantum Systems","authors":"Matteo Gallone, Beatrice Langella","doi":"10.1007/s10955-024-03313-9","DOIUrl":"https://doi.org/10.1007/s10955-024-03313-9","url":null,"abstract":"<p>We study conservation laws of a general class of quantum many-body systems subjected to an external time dependent quasi-periodic driving. When the frequency of the driving is large enough or the strength of the driving is small enough, we prove a Nekhoroshev-type stability result: we show that the system exhibits a prethermal state for stretched exponentially long times in the perturbative parameter. Moreover, we prove the quasi-conservation of the constants of motion of the unperturbed Hamiltonian and we analyze their physical meaning in examples of relevance to condensed matter and statistical physics.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940093","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}
引用次数: 0
Phase Transition of Eigenvalues in Deformed Ginibre Ensembles II: GinSE 变形吉尼布雷集合中特征值的相变 II：GinSE
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-08-08 DOI: 10.1007/s10955-024-03318-4
Dang-Zheng Liu, Lu Zhang
{"title":"Phase Transition of Eigenvalues in Deformed Ginibre Ensembles II: GinSE","authors":"Dang-Zheng Liu, Lu Zhang","doi":"10.1007/s10955-024-03318-4","DOIUrl":"https://doi.org/10.1007/s10955-024-03318-4","url":null,"abstract":"","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929262","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}
引用次数: 0
Spin Glass to Paramagnetic Transition and Triple Point in Spherical SK Model 球形 SK 模型中的自旋玻璃到顺磁转变和三重点
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-08-08 DOI: 10.1007/s10955-024-03296-7
Iain M. Johnstone, Yegor Klochkov, A. Onatski, Damian Pavlyshyn
{"title":"Spin Glass to Paramagnetic Transition and Triple Point in Spherical SK Model","authors":"Iain M. Johnstone, Yegor Klochkov, A. Onatski, Damian Pavlyshyn","doi":"10.1007/s10955-024-03296-7","DOIUrl":"https://doi.org/10.1007/s10955-024-03296-7","url":null,"abstract":"","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928247","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}
引用次数: 0
Random Normal Matrices: Eigenvalue Correlations Near a Hard Wall 随机正态矩阵：硬墙附近的特征值相关性
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-08-08 DOI: 10.1007/s10955-024-03314-8
Yacin Ameur, Christophe Charlier, Joakim Cronvall
{"title":"Random Normal Matrices: Eigenvalue Correlations Near a Hard Wall","authors":"Yacin Ameur, Christophe Charlier, Joakim Cronvall","doi":"10.1007/s10955-024-03314-8","DOIUrl":"https://doi.org/10.1007/s10955-024-03314-8","url":null,"abstract":"<p>We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant <span>(Gamma =2)</span> and that the number <i>n</i> of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order 1/<i>n</i> from the hard edge. At distances much larger than <span>(1/sqrt{n})</span>, the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the “semi-hard edge”. More precisely, we provide asymptotics for the correlation kernel <span>(K_{n}(z,w))</span> as <span>(nrightarrow infty )</span> in two microscopic regimes (with either <span>(|z-w| = mathcal{O}(1/sqrt{n}))</span> or <span>(|z-w| = mathcal{O}(1/n))</span>), as well as in three macroscopic regimes (with <span>(|z-w| asymp 1)</span>). For some of these regimes, the asymptotics involve oscillatory theta functions and weighted Szegő kernels.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141939965","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}
引用次数: 0
Large Deviations of Invariant Measures of Stochastic Reaction–Diffusion Equations on Unbounded Domains 无界域上随机反应-扩散方程不变量的大偏差
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-08-03 DOI: 10.1007/s10955-024-03316-6
Bixiang Wang
{"title":"Large Deviations of Invariant Measures of Stochastic Reaction–Diffusion Equations on Unbounded Domains","authors":"Bixiang Wang","doi":"10.1007/s10955-024-03316-6","DOIUrl":"https://doi.org/10.1007/s10955-024-03316-6","url":null,"abstract":"<p>This paper is concerned with the large deviation principle of invariant measures of the stochastic reaction–diffusion equation with polynomial drift driven by additive noise defined on the entire space <span>(mathbb {R}^n)</span>. Since the standard Sobolev embeddings on <span>(mathbb {R}^n)</span> are not compact and the spectrum of the Laplace operator on <span>(mathbb {R}^n)</span> are not discrete, there are many issues for proving the large deviations of invariant measures in the case of unbounded domains, including the difficulties for proving the compactness of the level sets of rate functions, the uniform Dembo–Zeitouni large deviations on compact sets as well as the exponential tightness on compact sets. Currently, there is no result available in the literature on the large deviations of invariant measures for stochastic PDEs on unbounded domains, and this paper is the first one to deal with this issue. The non-compactness of the standard Sobolev embeddings on <span>(mathbb {R}^n)</span> is circumvented by the idea of uniform tail-ends estimates together with the arguments of weighted spaces.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886098","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}
引用次数: 0
A Novel ES-BGK Model for Non-polytropic Gases with Internal State Density Independent of the Temperature 内部状态密度与温度无关的非多向气体新型 ES-BGK 模型
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-07-30 DOI: 10.1007/s10955-024-03286-9
Takashi Arima, Andrea Mentrelli, Tommaso Ruggeri
{"title":"A Novel ES-BGK Model for Non-polytropic Gases with Internal State Density Independent of the Temperature","authors":"Takashi Arima, Andrea Mentrelli, Tommaso Ruggeri","doi":"10.1007/s10955-024-03286-9","DOIUrl":"https://doi.org/10.1007/s10955-024-03286-9","url":null,"abstract":"<p>A novel ES-BGK-based model of non-polytropic rarefied gases in the framework of kinetic theory is presented. Key features of this model are: an internal state density function depending only on the microscopic energy of internal modes (avoiding the dependence on temperature seen in previous reference studies); full compliance with the H-theorem; feasibility of the closure of the system of moment equations based on the maximum entropy principle, following the well-established procedure of rational extended thermodynamics. The structure of planar shock waves in carbon dioxide (CO<span>(_2)</span>) obtained with the present model is in general good agreement with that of previous results, except for the computed internal temperature profile, which is qualitatively different with respect to the results obtained in previous studies, showing here a consistently monotonic behavior across the shock structure, rather than the non monotonic behavior previously found.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869310","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}
引用次数: 0
Maximum of the Gaussian Interface Model in Random External Fields 随机外场中高斯界面模型的最大值
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-07-27 DOI: 10.1007/s10955-024-03309-5
Hironobu Sakagawa
{"title":"Maximum of the Gaussian Interface Model in Random External Fields","authors":"Hironobu Sakagawa","doi":"10.1007/s10955-024-03309-5","DOIUrl":"https://doi.org/10.1007/s10955-024-03309-5","url":null,"abstract":"<p>We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on <span>(mathbb {R}^{Lambda _N})</span>, <span>(Lambda _N=[-N, N]^dcap mathbb {Z}^d)</span> with Hamiltonian <span>(H_N(phi )= frac{1}{4d}sum limits _{xsim y}(phi (x)-phi (y))^2 -sum limits _{xin Lambda _N}eta (x)phi (x))</span> and 0-boundary conditions. <span>({eta (x)}_{xin mathbb {Z}^d})</span> is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable <span>(eta (x))</span> when <span>(dge 5)</span>. In particular, we identify the leading order asymptotics of the maximum.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772163","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}
引用次数: 0
Maximal Codimension Collisions and Invariant Measures for Hard Spheres on a Line 直线上硬球的最大标度碰撞和不变度量
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-07-26 DOI: 10.1007/s10955-024-03310-y
Mark Wilkinson
{"title":"Maximal Codimension Collisions and Invariant Measures for Hard Spheres on a Line","authors":"Mark Wilkinson","doi":"10.1007/s10955-024-03310-y","DOIUrl":"https://doi.org/10.1007/s10955-024-03310-y","url":null,"abstract":"<p>For any <span>(Nge 3)</span>, we study invariant measures of the dynamics of <i>N</i> hard spheres whose centres are constrained to lie on a line. In particular, we study the invariant submanifold <span>(mathcal {M})</span> of the tangent bundle of the hard sphere billiard table comprising initial data that lead to the simultaneous collision of all <i>N</i> hard spheres. Firstly, we obtain a characterisation of those continuously-differentiable <i>N</i>-body scattering maps which generate a billiard dynamics on <span>(mathcal {M})</span> admitting a canonical weighted Hausdorff measure on <span>(mathcal {M})</span> (that we term the <i>Liouville measure on</i> <span>(mathcal {M})</span>) as an invariant measure. We do this by deriving a second boundary-value problem for a fully nonlinear PDE that all such scattering maps satisfy by necessity. Secondly, by solving a family of functional equations, we find sufficient conditions on measures which are absolutely continuous with respect to the Hausdorff measure in order that they be invariant for billiard flows that conserve momentum and energy. Finally, we show that the unique momentum- and energy-conserving <i>linear</i> <i>N</i>-body scattering map yields a billiard dynamics which admits the Liouville measure on <span>(mathcal {M})</span> as an invariant measure.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772165","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}
引用次数: 0
Time Evolution of the Boltzmann Entropy for a Nonequilibrium Dilute Gas 非平衡稀薄气体的玻尔兹曼熵的时间演变
IF 1.6 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-07-26 DOI: 10.1007/s10955-024-03311-x
Pedro L. Garrido, Sheldon Goldstein, David A. Huse, Joel L. Lebowitz
{"title":"Time Evolution of the Boltzmann Entropy for a Nonequilibrium Dilute Gas","authors":"Pedro L. Garrido, Sheldon Goldstein, David A. Huse, Joel L. Lebowitz","doi":"10.1007/s10955-024-03311-x","DOIUrl":"https://doi.org/10.1007/s10955-024-03311-x","url":null,"abstract":"<p>We investigate the time evolution of the Boltzmann entropy of a dilute gas of <i>N</i> particles, <span>(Ngg 1)</span>, as it undergoes a free expansion doubling its volume. The microstate of the system changes in time via Hamiltonian dynamics. Its entropy, at any time <i>t</i>, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time <i>t</i>. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells <span>(Delta _alpha )</span>. The initial and final macrostates of the system are thermal equilibrium states in volumes <i>V</i> and 2<i>V</i>, with the same energy <i>E</i> and particle number <i>N</i>. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the <span>(Delta _alpha )</span>. The intermediate (non-equilibrium) entropy does however depend on the size of the cells <span>(Delta _alpha )</span>. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining <span>(Delta v)</span>: it produces entropy at a rate proportional to <span>(Delta v)</span>. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of <span>(Delta v)</span> and is given by the Boltzmann equation for the limit <span>(Delta vrightarrow 0)</span>. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772164","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}
引用次数: 0
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