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The Effect of Spatial Disorder on Eigenvalue Statistics and Eigenstate Structure in a Simple Quantum System 空间无序对简单量子系统本征值统计量和本征态结构的影响
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-30 DOI: 10.1007/s10955-025-03449-2
Todd K. Timberlake, Noah C. Koch
{"title":"The Effect of Spatial Disorder on Eigenvalue Statistics and Eigenstate Structure in a Simple Quantum System","authors":"Todd K. Timberlake,&nbsp;Noah C. Koch","doi":"10.1007/s10955-025-03449-2","DOIUrl":"10.1007/s10955-025-03449-2","url":null,"abstract":"<div><p>We examine the effect of introducing spatial disorder on the energy eigenvalue statistics and eigenstate structure for a particle in an infinite square well of width <i>L</i> with twelve Dirac delta barriers placed inside. When the barriers are placed at regular intervals the distribution of spacings does not match any standard distribution and the eigenstates are generally delocalized. Spatial disorder is introduced through random barrier displacements drawn from a Gaussian distribution with mean zero and standard deviation <span>(sigma L)</span>. As <span>(sigma )</span> is increased the system becomes disordered and the resulting level spacing distribution depends on the transmission probability <i>T</i> through each barrier: Poisson-like for <span>(Tapprox 0)</span>, a Brody distribution for <span>(T=0.5)</span>, a Wigner GOE distribution for <span>(Tapprox 0.7)</span>, and Gaussian for <span>(Tapprox 1)</span>. The transition in the level spacing statistics takes place over a range of approximately <span>(10^{-4}&lt; sigma &lt; 10^{-3})</span> in all cases, with the reduced chi-square values for the fit to the relevant distribution following a power law in <span>(sigma )</span> within the transition range. These results show that even a small degree of spatial disorder (two orders of magnitude smaller than the distance between barriers) is sufficient to produce eigenvalue statistics that match the limiting distribution for the highly disordered system. In addition, as disorder is increased the eigenstates become strongly localized for <span>(Tapprox 0)</span>, but remain delocalized for <span>(Tapprox 1)</span> and show only weak localization at intermediate values of <i>T</i>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03449-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888765","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}
引用次数: 0
Precise Deviations for Branches of the Random Binary Tree in the Horton–Strahler Analysis Horton-Strahler分析中随机二叉树分支的精确偏差
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-29 DOI: 10.1007/s10955-025-03448-3
Fuqing Gao, Zhi Qu, Youzhou Zhou
{"title":"Precise Deviations for Branches of the Random Binary Tree in the Horton–Strahler Analysis","authors":"Fuqing Gao,&nbsp;Zhi Qu,&nbsp;Youzhou Zhou","doi":"10.1007/s10955-025-03448-3","DOIUrl":"10.1007/s10955-025-03448-3","url":null,"abstract":"<div><p>In this paper, we study the precise deviations for the number of branches of a random binary tree in the context of Horton–Strahler analysis. We establish precise large deviations, precise moderate deviations, and Cramér-type moderate deviations for the number of branches of the random binary tree. As a consequence of the Cramér-type moderate deviations, a Berry–Esseen bound is derived. The derivations of these results rely heavily on asymptotic analysis of certain discrete summations.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888665","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
Derivation and Analysis of a Class of Relaxation Operators in Kinetic Theory 运动理论中一类松弛算子的推导与分析
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-24 DOI: 10.1007/s10955-025-03419-8
Stéphane Brull, Vincent Pavan, Jacques Schneider
{"title":"Derivation and Analysis of a Class of Relaxation Operators in Kinetic Theory","authors":"Stéphane Brull,&nbsp;Vincent Pavan,&nbsp;Jacques Schneider","doi":"10.1007/s10955-025-03419-8","DOIUrl":"10.1007/s10955-025-03419-8","url":null,"abstract":"<div><p>We aim to present a theory for the derivation of a class of relaxation operators approximating the Boltzmann collision operator. The construction is based on an approximation of the inverse Boltzmann linearized operator, on relaxation equations on the moments of the distribution function and finally on a variational problem to be solved. The theory comprises a characterization of the set of moments of non negative integrable functions, a study of those linear application whose range lies in this set and a generalization of the functional to be minimized under moment constraints. In particular we clarify but also modify some steps in the proof of Junk’s theorem on the characterization of moments of non negative functions (Junk in Math Models Methods Appl Sci 10:1001–1025, 2000). We also reestablish a theorem of Csiszar’s (Acta Math Hung 68:161–185, 1995) by different means on a class of functionals leading to well-posed variational problems. The present theory encompasses the derivation of known models and that of new models.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871416","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
Specific Heat of the Driven Curie–Weiss Model 驱动居里-魏斯模型的比热
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-22 DOI: 10.1007/s10955-025-03438-5
Elena Rufeil Fiori, Christian Maes, Robbe Vidts
{"title":"Specific Heat of the Driven Curie–Weiss Model","authors":"Elena Rufeil Fiori,&nbsp;Christian Maes,&nbsp;Robbe Vidts","doi":"10.1007/s10955-025-03438-5","DOIUrl":"10.1007/s10955-025-03438-5","url":null,"abstract":"<div><p>Applying a time-periodic magnetic field to the standard ferromagnetic Curie–Weiss model brings the spin system in a steady out-of-equilibrium condition. We recall how the hysteresis gets influenced by the amplitude and the frequency of that field, and how an amplitude- and frequency-dependent (dynamical) critical temperature can be discerned. The dissipated power measures the area of the hysteresis loop and changes with temperature. The excess heat determines a nonequilibrium specific heat giving the quasistatic thermal response. We compute that specific heat, which appears to diverge at the critical temperature, quite different from the equilibrium case.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143861374","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
Density-Functional Theory for the Dicke Hamiltonian 迪克哈密顿的密度函数理论
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-21 DOI: 10.1007/s10955-025-03442-9
Vebjørn H. Bakkestuen, Mihály A. Csirik, Andre Laestadius, Markus Penz
{"title":"Density-Functional Theory for the Dicke Hamiltonian","authors":"Vebjørn H. Bakkestuen,&nbsp;Mihály A. Csirik,&nbsp;Andre Laestadius,&nbsp;Markus Penz","doi":"10.1007/s10955-025-03442-9","DOIUrl":"10.1007/s10955-025-03442-9","url":null,"abstract":"<div><p>A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a Hohenberg–Kohn theorem that manifests the magnetization and displacement as internal variables, along with several representability results. The constrained-search functionals for pure states and ensembles are introduced and analyzed. We find the optimizers for the pure-state constrained-search functional to be low-lying eigenstates of the Hamiltonian and, based on the properties of the optimizers, we formulate an adiabatic-connection formula. In the reduced case of the Rabi model we can even show differentiability of the universal density functional, which amounts to unique pure-state <i>v</i>-representability.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03442-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856621","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}
引用次数: 0
Rotational Entropy for Random Torus Maps 随机环面映射的旋转熵
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-21 DOI: 10.1007/s10955-025-03443-8
Weifeng Jiang, Zhengxing Lian, Yujun Zhu
{"title":"Rotational Entropy for Random Torus Maps","authors":"Weifeng Jiang,&nbsp;Zhengxing Lian,&nbsp;Yujun Zhu","doi":"10.1007/s10955-025-03443-8","DOIUrl":"10.1007/s10955-025-03443-8","url":null,"abstract":"<div><p>In this paper, the rotational entropy <span>(h_r(varphi ))</span> is investigated for a random dynamical system <span>(varphi )</span> on the torus. The formula of <span>(h_r(varphi ))</span> is obtained for <span>(varphi )</span> which satisfies certain assumptions, and the lower and upper bounds of <span>(h_r(varphi ))</span> are given for more general <span>(varphi )</span>. Several examples are presented to show that these results may not hold without the assumptions. This work can be seen as a random version of the previous work (Jiang et al. in J Differ Equ 379:862–883, 2024), in which the rotational entropy was introduced and investigated as a homotopy invariant for any torus map.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143852594","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
Weighted Sequence Entropy and Maximal Pattern Entropy 加权序列熵和最大模式熵
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-21 DOI: 10.1007/s10955-025-03445-6
Xiaoxiao Nie, Yu Huang
{"title":"Weighted Sequence Entropy and Maximal Pattern Entropy","authors":"Xiaoxiao Nie,&nbsp;Yu Huang","doi":"10.1007/s10955-025-03445-6","DOIUrl":"10.1007/s10955-025-03445-6","url":null,"abstract":"<div><p>As an extension of weighted entropy, the weighted topological sequence entropy and the weighted measure-theoretic sequence entropy are defined. A variational principle of relating the two weighted sequence entropies is established. The weighted maximal pattern entropy is also defined. It is shown that for homeomorphism dynamical systems the weighted maximal pattern entropy is equal to the supremum of the weighted sequence entropies over all strictly increasing sequences in integers both in topological and measure-theoretic settings.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856671","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 Nonlinear, Conservative, Entropic Fokker–Planck Model for Multi-species Collisions 多物种碰撞的非线性、保守、熵Fokker-Planck模型
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-17 DOI: 10.1007/s10955-025-03436-7
Evan Habbershaw, Cory D. Hauck, Jingwei Hu, Jeffrey R. Haack
{"title":"A Nonlinear, Conservative, Entropic Fokker–Planck Model for Multi-species Collisions","authors":"Evan Habbershaw,&nbsp;Cory D. Hauck,&nbsp;Jingwei Hu,&nbsp;Jeffrey R. Haack","doi":"10.1007/s10955-025-03436-7","DOIUrl":"10.1007/s10955-025-03436-7","url":null,"abstract":"<div><p>A multi-species Fokker–Planck model for simulating particle collisions in a plasma is presented. The model includes various parameters that must be tuned. Under reasonable assumptions on these parameters, the model satisfies appropriate conservation laws, dissipates an entropy, and satisfies an <span>(mathcal {H})</span>-Theorem. In addition, the model parameters provide the additional flexibility that is used to match simultaneously momentum and temperature relaxation formulas derived from the Boltzmann collision operator for a binary mixture with Coulomb potential. A numerical method for solving the resulting space-homogeneous kinetic equation is presented and two examples are provided to demonstrate the relaxation of species bulk velocities and temperatures to their equilibrium values.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840293","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
The Intertwining Property for Laguerre Processes with a Fixed Parameter 具有固定参数的Laguerre过程的缠绕特性
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-16 DOI: 10.1007/s10955-025-03441-w
Alexander I. Bufetov, Yosuke Kawamoto
{"title":"The Intertwining Property for Laguerre Processes with a Fixed Parameter","authors":"Alexander I. Bufetov,&nbsp;Yosuke Kawamoto","doi":"10.1007/s10955-025-03441-w","DOIUrl":"10.1007/s10955-025-03441-w","url":null,"abstract":"<div><p>We investigate the intertwining of Laguerre processes of parameter <span>(alpha )</span> in different dimensions. We introduce a Feller kernel that depends on <span>(alpha )</span> and intertwines the <span>(alpha )</span>-Laguerre process in <span>(N+1)</span> dimensions and that in <i>N</i> dimensions. When <span>(alpha )</span> is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order <span>((N+alpha +1) times (N+1))</span> are fixed, then the those of its <span>((N+alpha ) times N )</span> truncation matrix are given by the new kernel.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03441-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840359","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}
引用次数: 0
Trajectory Class Fluctuation Theorem 轨迹类涨落定理
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-04-11 DOI: 10.1007/s10955-025-03422-z
Gregory Wimsatt, Alexander B. Boyd, James P. Crutchfield
{"title":"Trajectory Class Fluctuation Theorem","authors":"Gregory Wimsatt,&nbsp;Alexander B. Boyd,&nbsp;James P. Crutchfield","doi":"10.1007/s10955-025-03422-z","DOIUrl":"10.1007/s10955-025-03422-z","url":null,"abstract":"<div><p>The Trajectory Class Fluctuation Theorem (TCFT) presents equalities between thermodynamic quantities, such as work costs and free energy changes, and the probabilities of classes of system-state trajectories in equilibrium-steady-state nonequilibrium processes. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks’ Detailed Fluctuation Theorem (single trajectories) to Jarzynski’s Equality (full trajectory ensembles). Leveraging coarse-grained information about how systems evolve, the TCFT provides a substantial strengthening of the Second Law of Thermodynamics—that, in point of fact, can be a rather weak bound between requisite work and free energy change. It also can be used to improve empirical estimates of free energies, a task known to be statistically challenging, by diverting attention from rare, work-dominant trajectories in convenient but highly nonequilibrium processes. The TCFT also reveals new forms of free energy useful for bounding work costs when computing with systems whose microscopic details are difficult to ascertain—forms that can be solved analytically and practically estimated. For engineered systems more generally, it connects the role of system state trajectories in system functionality to the particular work costs required to evolve those trajectories. Previously, the TCFT was used to connect the microscopic dynamics of experimentally-implemented Josephson-junction information engines with the mesoscopic descriptions of how information was processed. The development here justifies that empirical analysis, explicating its mathematical foundations.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03422-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143822014","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}
引用次数: 0
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