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The Radius of a Self-repelling Star Polymer 自排斥星形聚合物的半径
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-05-06 DOI: 10.1007/s10955-025-03444-7
Carl Mueller, Eyal Neuman
{"title":"The Radius of a Self-repelling Star Polymer","authors":"Carl Mueller,&nbsp;Eyal Neuman","doi":"10.1007/s10955-025-03444-7","DOIUrl":"10.1007/s10955-025-03444-7","url":null,"abstract":"<div><p>We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes <i>N</i> Brownian motions up to time <i>T</i>, started at the origin and subject to exponential penalization based on the amount of time they spend close to each other, or close to themselves. The effective radius measures the typical distance from the origin. Our main result gives estimates for the effective radius where in two and three dimensions we impose the restriction that <span>(T le N)</span>. One of the highlights of our results is that in two dimensions, we find that the radius is proportional to <span>(T^{3/4})</span>, up to logarithmic corrections.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03444-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908668","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
Bounds on (T_c) in the Eliashberg Theory of Superconductivity. I: The (gamma )-Model Eliashberg超导理论中(T_c)的边界。I: (gamma ) -模型
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-05-06 DOI: 10.1007/s10955-025-03446-5
M. K.-H. Kiessling, B. L. Altshuler, E. A. Yuzbashyan
{"title":"Bounds on (T_c) in the Eliashberg Theory of Superconductivity. I: The (gamma )-Model","authors":"M. K.-H. Kiessling,&nbsp;B. L. Altshuler,&nbsp;E. A. Yuzbashyan","doi":"10.1007/s10955-025-03446-5","DOIUrl":"10.1007/s10955-025-03446-5","url":null,"abstract":"<div><p>Using the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature <span>(T_c)</span> are obtained for the <span>(gamma )</span> model—a version of Eliashberg theory in which the effective electron–electron interaction is proportional to <span>((g/|omega _n-omega _m|)^{gamma })</span>, where <span>(omega _n-omega _m)</span> is the transferred Matsubara frequency, <span>(g&gt;0)</span> a reference energy, and <span>(gamma &gt;0)</span> a parameter. The rigorous lower bounds are based on a variational principle that identifies <span>((2pi T_c/g)^gamma )</span> with the largest (positive) eigenvalue <span>(mathfrak {g}(gamma ))</span> of an explicitly constructed compact, self-adjoint operator <span>(mathfrak {G}(gamma ))</span>. These lower bounds form an increasing sequence that converges to <span>(T_c(g,gamma ))</span>. The upper bound on <span>(T_c(g,gamma ))</span> is based on fixed point theory, proving linear stability of the normal state for <i>T</i> larger than the upper bound on <span>(T_c(g,gamma ))</span>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03446-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908667","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
Analytical Methods for Continuous Attractor Neural Networks 连续吸引子神经网络的分析方法
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2025-05-02 DOI: 10.1007/s10955-025-03447-4
Martino Salomone Centonze, Alessandro Treves, Elena Agliari, Adriano Barra
{"title":"Analytical Methods for Continuous Attractor Neural Networks","authors":"Martino Salomone Centonze,&nbsp;Alessandro Treves,&nbsp;Elena Agliari,&nbsp;Adriano Barra","doi":"10.1007/s10955-025-03447-4","DOIUrl":"10.1007/s10955-025-03447-4","url":null,"abstract":"<div><p>Pyramidal cells that emit spikes when the animal is at specific locations of the environment are known as <i>place cells</i>: these neurons are thought to provide an internal representation of space via <i>cognitive maps</i>. Here, we consider the Battaglia-Treves neural network model for cognitive map storage and reconstruction, instantiated with McCulloch &amp; Pitts binary neurons. To quantify the information processing capabilities of these networks, we exploit spin-glass techniques, namely the <i>interpolation method</i> and the <i>replica trick</i>. In particular, in the low-storage regime (i.e., when the number of stored maps scales sub-linearly with the network size and the order parameters self-average around their means), by adapting the Hamilton-Jacobi PDE-approach, we obtain an exact phase diagram in the noise vs inhibition strength plane. In the high-storage regime, by adapting the standard interpolation based on stochastic stability, we find that—for mild inhibition and not too high noise—memorization and retrieval of an extensive number of spatial maps is possible. These results, holding under the replica-symmetry assumption, are recovered, for completeness, also by the replica method and they are corroborated by Monte Carlo simulations. Finally, by leveraging the integral representation of the model (in terms of a bipartite network equipped with highly-selective hidden units), we successfully test its robustness versus various distributions of place fields, including the log-normal distribution observed in recent experiments on bats navigating long tunnels. Additionally, we demonstrate that, by appropriately coupling these hidden units, the network can effectively orient itself even in dynamic environments.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03447-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900662","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
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
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