Pub Date : 2024-02-21DOI: 10.1007/s10955-024-03240-9
Abstract
We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of reversible models for which the product invariant measure is known and the gradient condition is satisfied so that we can explicitly compute the transport coefficients associated to the diffusive hydrodynamic rescaling. Based on the Macroscopic Fluctuation Theory (Bertini et al. in Rev Mod Phys 87:593–636, 2015) we have that the large deviations rate functional for a stationary non equilibrium state can be computed solving a Hamilton–Jacobi equation depending only on the transport coefficients and the details of the boundary sources. Thus, we are able to identify a class of models having transport coefficients for which the Hamilton–Jacobi equation can indeed be solved. We give a complete characterization in the case of generalized zero range models and discuss several other cases. For the generalized zero range models we identify a class of discrete models that, modulo trivial extensions, coincides with the class discussed in Frassek and Giardinà (J Math Phys 63(10):103301–103335, 2022) and a class of continuous dynamics that coincides with the class in Franceschini et al. (J Math Phys 64(4): 043304–043321, 2023). Along the discussion we obtain a complete characterization of reversible misanthrope processes solving the discrete equations in Cocozza-Thivent (Z Wahrsch Verw Gebiete 70(4):509–523, 1985).
摘要 我们考虑了一系列模型,这些模型的每个点上都有任意正质量量,并随机地与近邻点交换任意质量量。我们只考虑扩散模型。我们确定了一类已知乘积不变度量且满足梯度条件的可逆模型,这样我们就可以明确计算与扩散流体力学重缩相关的输运系数。基于宏观波动理论(Bertini 等人,Rev Mod Phys 87:593-636, 2015),我们可以计算出静止非平衡态的大偏差率函数,只需求解一个汉密尔顿-贾科比方程,而这取决于传输系数和边界源的细节。因此,我们能够确定一类具有传输系数的模型,其汉密尔顿-雅可比方程确实可以求解。我们给出了广义零范围模型的完整特征,并讨论了其他几种情况。对于广义零范围模型,我们确定了一类离散模型,其模态琐碎扩展与 Frassek 和 Giardinà (J Math Phys 63(10):103301-103335, 2022) 中讨论的一类模型相吻合;我们还确定了一类连续动力学模型,其模态琐碎扩展与 Franceschini 等人 (J Math Phys 64(4):043304-043321, 2023).随着讨论的深入,我们获得了求解 Cocozza-Thivent (Z Wahrsch Verw Gebiete 70(4): 509-523, 1985) 中离散方程的可逆厌世过程的完整表征。
{"title":"On a Class of Solvable Stationary Non Equilibrium States for Mass Exchange Models","authors":"","doi":"10.1007/s10955-024-03240-9","DOIUrl":"https://doi.org/10.1007/s10955-024-03240-9","url":null,"abstract":"<h3>Abstract</h3> <p>We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of reversible models for which the product invariant measure is known and the gradient condition is satisfied so that we can explicitly compute the transport coefficients associated to the diffusive hydrodynamic rescaling. Based on the Macroscopic Fluctuation Theory (Bertini et al. in Rev Mod Phys 87:593–636, 2015) we have that the large deviations rate functional for a stationary non equilibrium state can be computed solving a Hamilton–Jacobi equation depending only on the transport coefficients and the details of the boundary sources. Thus, we are able to identify a class of models having transport coefficients for which the Hamilton–Jacobi equation can indeed be solved. We give a complete characterization in the case of generalized zero range models and discuss several other cases. For the generalized zero range models we identify a class of discrete models that, modulo trivial extensions, coincides with the class discussed in Frassek and Giardinà (J Math Phys 63(10):103301–103335, 2022) and a class of continuous dynamics that coincides with the class in Franceschini et al. (J Math Phys 64(4): 043304–043321, 2023). Along the discussion we obtain a complete characterization of reversible misanthrope processes solving the discrete equations in Cocozza-Thivent (Z Wahrsch Verw Gebiete 70(4):509–523, 1985).</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139917963","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}
Pub Date : 2024-02-20DOI: 10.1007/s10955-024-03235-6
R. S. Kharwanlang, Elisheba Syiem
We analytically investigate the zero-temperature hysteresis loops in a one-dimensional 3-state clock model in the low disorder limit, incorporating dilution and quenched spins. Utilizing a probabilistic approach with continuous random fields, we study the behavior of the model at nearly zero frequency limit of the applied field and confirming our analytical results via simulations. Dilution reproduces distorted hysteresis loop shapes akin to those in geological magnetic rocks, while quenched spins significantly contribute to hysteresis loop asymmetry.
{"title":"Study of the Hysteretic Response with Dilution and Quenched Spins in the Low Disorder Limit of the Random Field 3-State Clock Model at Zero Temperature","authors":"R. S. Kharwanlang, Elisheba Syiem","doi":"10.1007/s10955-024-03235-6","DOIUrl":"https://doi.org/10.1007/s10955-024-03235-6","url":null,"abstract":"<p>We analytically investigate the zero-temperature hysteresis loops in a one-dimensional 3-state clock model in the low disorder limit, incorporating dilution and quenched spins. Utilizing a probabilistic approach with continuous random fields, we study the behavior of the model at nearly zero frequency limit of the applied field and confirming our analytical results via simulations. Dilution reproduces distorted hysteresis loop shapes akin to those in geological magnetic rocks, while quenched spins significantly contribute to hysteresis loop asymmetry.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139917959","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}
Pub Date : 2024-02-17DOI: 10.1007/s10955-024-03239-2
Mengmeng Wang, Dong Su, Wei Wang
This paper develops an averaging approach on macroscopic scales to derive Smoluchowski–Kramers approximation for a Langevin equation with state dependent friction in d-dimensional space. In this approach we couple the microscopic dynamics to the macroscopic scales. The weak convergence rate is also presented.
本文开发了一种宏观尺度上的平均方法,以推导出 d 维空间中具有状态相关摩擦力的朗文方程的 Smoluchowskii-Kramers 近似值。在这种方法中,我们将微观动力学与宏观尺度结合起来。我们还提出了弱收敛率。
{"title":"Averaging on Macroscopic Scales with Application to Smoluchowski–Kramers Approximation","authors":"Mengmeng Wang, Dong Su, Wei Wang","doi":"10.1007/s10955-024-03239-2","DOIUrl":"https://doi.org/10.1007/s10955-024-03239-2","url":null,"abstract":"<p>This paper develops an averaging approach on macroscopic scales to derive Smoluchowski–Kramers approximation for a Langevin equation with state dependent friction in <i>d</i>-dimensional space. In this approach we couple the microscopic dynamics to the macroscopic scales. The weak convergence rate is also presented.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903773","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}
Pub Date : 2024-02-15DOI: 10.1007/s10955-024-03237-4
Giorgio Cipolloni, Nicolo Grometto
The dissipative spectral form factor (DSFF), recently introduced in Li et al. (Phys Rev Lett 127(17):170602, 2021) for the Ginibre ensemble, is a key tool to study universal properties of dissipative quantum systems. In this work we compute the DSFF for a large class of random matrices with real or complex entries up to an intermediate time scale, confirming the predictions from Li et al. (Phys Rev Lett 127(17):170602, 2021). The analytic formula for the DSFF in the real case was previously unknown. Furthermore, we show that for short times the connected component of the DSFF exhibits a non-universal correction depending on the fourth cumulant of the entries. These results are based on the central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices Cipolloni et al. (Electron J Prob 26:1–61, 2021) and Cipolloni et al. (Commun Pure Appl Math 76(5): 946–1034, 2023).
李等人(Phys Rev Lett 127(17):170602, 2021)最近针对吉尼布雷集合提出的耗散谱形式因子(DSFF)是研究耗散量子系统普遍特性的关键工具。在这项工作中,我们计算了一大类具有实数或复数条目的随机矩阵的 DSFF,直至中间时间尺度,证实了 Li 等人的预测(Phys Rev Lett 127(17):170602, 2021)。实数情况下 DSFF 的解析公式以前是未知的。此外,我们还证明,在短时间内,DSFF 的连通分量表现出一种非普遍的修正,这取决于条目的第四积。这些结果基于 Cipolloni 等人(Electron J Prob 26:1-61, 2021)和 Cipolloni 等人(Commun Pure Appl Math 76(5):946-1034, 2023).
{"title":"The Dissipative Spectral Form Factor for I.I.D. Matrices","authors":"Giorgio Cipolloni, Nicolo Grometto","doi":"10.1007/s10955-024-03237-4","DOIUrl":"https://doi.org/10.1007/s10955-024-03237-4","url":null,"abstract":"<p>The dissipative spectral form factor (DSFF), recently introduced in Li et al. (Phys Rev Lett 127(17):170602, 2021) for the Ginibre ensemble, is a key tool to study universal properties of dissipative quantum systems. In this work we compute the DSFF for a large class of random matrices with real or complex entries up to an intermediate time scale, confirming the predictions from Li et al. (Phys Rev Lett 127(17):170602, 2021). The analytic formula for the DSFF in the real case was previously unknown. Furthermore, we show that for short times the connected component of the DSFF exhibits a non-universal correction depending on the fourth cumulant of the entries. These results are based on the central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices Cipolloni et al. (Electron J Prob 26:1–61, 2021) and Cipolloni et al. (Commun Pure Appl Math 76(5): 946–1034, 2023).</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771918","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}
Pub Date : 2024-02-15DOI: 10.1007/s10955-023-03228-x
Marco Bianucci, Mauro Bologna, Riccardo Mannella
This paper deals with the problem of finding the Fokker Planck Equation (FPE) for the single-time probability density function (PDF) that optimally approximates the single-time PDF of a 1-D Stochastic Differential Equation (SDE) with Gaussian correlated noise. In this context, we tackle two main tasks. First, we consider the case of weak noise and in this framework we give a formal ground to the effective correction, introduced elsewhere (Bianucci and Mannella in J Phys Commun 4(10):105019, 2020, https://doi.org/10.1088/2399-6528/abc54e), to the Best Fokker Planck Equation (a standard “Born-Oppenheimer” result), also covering the more general cases of multiplicative SDE. Second, we consider the FPE obtained by using the Local Linearization Approach (LLA), and we show that a generalized cumulant approach allows an understanding of why the LLA FPE performs so well, even for noises with long (but finite) time scales and large intensities.
{"title":"About the Optimal FPE for Non-linear 1d-SDE with Gaussian Noise: The Pitfall of the Perturbative Approach","authors":"Marco Bianucci, Mauro Bologna, Riccardo Mannella","doi":"10.1007/s10955-023-03228-x","DOIUrl":"https://doi.org/10.1007/s10955-023-03228-x","url":null,"abstract":"<p>This paper deals with the problem of finding the Fokker Planck Equation (FPE) for the single-time probability density function (PDF) that optimally approximates the single-time PDF of a 1-D Stochastic Differential Equation (SDE) with Gaussian correlated noise. In this context, we tackle two main tasks. First, we consider the case of weak noise and in this framework we give a formal ground to the effective correction, introduced elsewhere (Bianucci and Mannella in J Phys Commun 4(10):105019, 2020, https://doi.org/10.1088/2399-6528/abc54e), to the Best Fokker Planck Equation (a standard “Born-Oppenheimer” result), also covering the more general cases of multiplicative SDE. Second, we consider the FPE obtained by using the Local Linearization Approach (LLA), and we show that a generalized cumulant approach allows an understanding of why the LLA FPE performs so well, even for noises with long (but finite) time scales and large intensities.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771817","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}
Pub Date : 2024-01-31DOI: 10.1007/s10955-023-03227-y
Abstract
We study the radius of gyration (R_T) of a self-repellent fractional Brownian motion (left{ B^H_tright} _{0le tle T}) taking values in (mathbb {R}^d). Our sharpest result is for (d=1), where we find that with high probability, $$begin{aligned} R_T asymp T^nu , quad text {with }quad nu =frac{2}{3}left( 1+Hright) . end{aligned}$$For (d>1), we provide upper and lower bounds for the exponent (nu ), but these bounds do not match.
Abstract We study the radius of gyration (R_T) of a self-repellent fractional Brownian motion (left{ B^H_tright} _{0le tle T}) taking values in (mathbb {R}^d) .我们最尖锐的结果是针对 (d=1)的,在这里我们发现很有可能, $$begin{aligned}R_T asymp T^nu , quad text {with }quad nu =frac{2}{3}left( 1+Hright).end{aligned}$$ 对于 (d>1), 我们提供了指数 (nu ) 的上下限,但是这些界限并不匹配。
{"title":"On the Radius of Self-Repellent Fractional Brownian Motion","authors":"","doi":"10.1007/s10955-023-03227-y","DOIUrl":"https://doi.org/10.1007/s10955-023-03227-y","url":null,"abstract":"<h3>Abstract</h3> <p>We study the radius of gyration <span> <span>(R_T)</span> </span> of a self-repellent fractional Brownian motion <span> <span>(left{ B^H_tright} _{0le tle T})</span> </span> taking values in <span> <span>(mathbb {R}^d)</span> </span>. Our sharpest result is for <span> <span>(d=1)</span> </span>, where we find that with high probability, <span> <span>$$begin{aligned} R_T asymp T^nu , quad text {with }quad nu =frac{2}{3}left( 1+Hright) . end{aligned}$$</span> </span>For <span> <span>(d>1)</span> </span>, we provide upper and lower bounds for the exponent <span> <span>(nu )</span> </span>, but these bounds do not match.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139644829","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}
Pub Date : 2024-01-29DOI: 10.1007/s10955-024-03233-8
Robert I. A. Patterson, D. R. Michiel Renger, Upanshu Sharma
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of the particle system. While large deviations can be studied in considerable generality, these variational structures are often restricted to systems in detailed balance. Using insights from macroscopic fluctuation theory, in this work we aim to generalise this variational connection beyond dissipative systems by augmenting densities with fluxes, which encode non-dissipative effects. Our main contribution is an abstract theory, which for a given flux-density cost and a quasipotential, provides a decomposition into dissipative and non-dissipative components and a generalised orthogonality relation between them. We then apply this abstract theory to various stochastic particle systems—independent copies of jump processes, zero-range processes, chemical-reaction networks in complex balance and lattice-gas models—without assuming detailed balance. For macroscopic equations arising out of these particle systems, we derive new variational formulations that generalise the classical gradient-flow formulation.
{"title":"Variational Structures Beyond Gradient Flows: a Macroscopic Fluctuation-Theory Perspective","authors":"Robert I. A. Patterson, D. R. Michiel Renger, Upanshu Sharma","doi":"10.1007/s10955-024-03233-8","DOIUrl":"https://doi.org/10.1007/s10955-024-03233-8","url":null,"abstract":"<p>Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of the particle system. While large deviations can be studied in considerable generality, these variational structures are often restricted to systems in detailed balance. Using insights from macroscopic fluctuation theory, in this work we aim to generalise this variational connection beyond dissipative systems by augmenting densities with fluxes, which encode non-dissipative effects. Our main contribution is an abstract theory, which for a given flux-density cost and a quasipotential, provides a decomposition into dissipative and non-dissipative components and a generalised orthogonality relation between them. We then apply this abstract theory to various stochastic particle systems—independent copies of jump processes, zero-range processes, chemical-reaction networks in complex balance and lattice-gas models—without assuming detailed balance. For macroscopic equations arising out of these particle systems, we derive new variational formulations that generalise the classical gradient-flow formulation.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582149","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}
Pub Date : 2024-01-28DOI: 10.1007/s10955-023-03225-0
S. Tamizhazhagan, Atul Kumar Verma
In traffic flow, flyovers play a vital role in reducing traffic congestion, advancing commute timing, and helping to prevent collision scenarios. Inspired by the real-life applications of flyover, we model a coupled two-lane transport system where the lanes are divided into three segments in which the particle lane switching mechanism executes only in the middle segment of the lane, and particle inclusion and expulsion kinetics are performed in first and last segment of the lane to embody the infrastructure of flyover. The nature of the system characteristics is analyzed for diverse values of particle inclusion, expulsion, and coupling rates through graphical diagrams of phase planes, density profiles, shock dynamics, and phase transitions. The time-invariant behavior of the system is inspected numerically by utilizing the well-known method of mean-field theory, and it is discovered that the biased dynamics of particle inclusion, expulsion, and fully asymmetric coupling condition yield the phase diagram to disclose more unanticipated mixed stationary phases. Besides, the system experiences the fruitful novel incident of the double shock phase when the possibility of particle inclusion occurs relatively higher than the expulsion event. Also, it is noticed that the system experiences the fascinating phenomenon of shock propagation by traveling in either vertical/horizontal direction in the shock region of the phase diagram under the symmetric coupling circumstance, such as the position of the shock suddenly transits from the right to left segment without crossing the middle segment. The calculated numerical results are in good agreement with Monte Carlo simulation.
{"title":"Biased Dynamics of Langmuir Kinetics and Coupling on Exclusion Process","authors":"S. Tamizhazhagan, Atul Kumar Verma","doi":"10.1007/s10955-023-03225-0","DOIUrl":"https://doi.org/10.1007/s10955-023-03225-0","url":null,"abstract":"<p>In traffic flow, flyovers play a vital role in reducing traffic congestion, advancing commute timing, and helping to prevent collision scenarios. Inspired by the real-life applications of flyover, we model a coupled two-lane transport system where the lanes are divided into three segments in which the particle lane switching mechanism executes only in the middle segment of the lane, and particle inclusion and expulsion kinetics are performed in first and last segment of the lane to embody the infrastructure of flyover. The nature of the system characteristics is analyzed for diverse values of particle inclusion, expulsion, and coupling rates through graphical diagrams of phase planes, density profiles, shock dynamics, and phase transitions. The time-invariant behavior of the system is inspected numerically by utilizing the well-known method of mean-field theory, and it is discovered that the biased dynamics of particle inclusion, expulsion, and fully asymmetric coupling condition yield the phase diagram to disclose more unanticipated mixed stationary phases. Besides, the system experiences the fruitful novel incident of the double shock phase when the possibility of particle inclusion occurs relatively higher than the expulsion event. Also, it is noticed that the system experiences the fascinating phenomenon of shock propagation by traveling in either vertical/horizontal direction in the shock region of the phase diagram under the symmetric coupling circumstance, such as the position of the shock suddenly transits from the right to left segment without crossing the middle segment. The calculated numerical results are in good agreement with Monte Carlo simulation.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582246","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}
Pub Date : 2024-01-28DOI: 10.1007/s10955-024-03231-w
Tong Xuan Nguyen, Roberto Fernández
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of “decoupling parameters”, advocated by Park (J. Stat. Phys. 27, 553–576 (1982)), which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a (beta )-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small (beta ). To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams Bissacot et al. (J. Stat. Phys. 139, 598–617 (2010)). As an application we show that our lower bound of the radius of (beta )-analyticity is larger than Park’s for quantum systems two-body interactions.
{"title":"High-Temperature Cluster Expansion for Classical and Quantum Spin Lattice Systems With Multi-Body Interactions","authors":"Tong Xuan Nguyen, Roberto Fernández","doi":"10.1007/s10955-024-03231-w","DOIUrl":"https://doi.org/10.1007/s10955-024-03231-w","url":null,"abstract":"<p>We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of “decoupling parameters”, advocated by Park (J. Stat. Phys. <b>27</b>, 553–576 (1982)), which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a <span>(beta )</span>-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small <span>(beta )</span>. To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams Bissacot et al. (J. Stat. Phys. <b>139</b>, 598–617 (2010)). As an application we show that our lower bound of the radius of <span>(beta )</span>-analyticity is larger than Park’s for quantum systems two-body interactions.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582252","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}
Pub Date : 2024-01-28DOI: 10.1007/s10955-023-03229-w
Zhang Chen, Xiaoxiao Sun, Dandan Yang
This paper is concerned with the stochastic reaction-diffusion lattice systems defined on the entire set with both locally Lipschitz nonlinear drift and diffusion terms. The central limit theorem is derived for such infinite-dimensional stochastic systems. Moreover, the moderate deviation principle of solution processes is also established by the weak convergence method based on the variational representation of positive functionals of Brownian motion. The method relies on proving the convergence of the solutions of the controlled stochastic lattice systems.
{"title":"Central Limit Theorems and Moderate Deviations for Stochastic Reaction-Diffusion Lattice Systems","authors":"Zhang Chen, Xiaoxiao Sun, Dandan Yang","doi":"10.1007/s10955-023-03229-w","DOIUrl":"https://doi.org/10.1007/s10955-023-03229-w","url":null,"abstract":"<p>This paper is concerned with the stochastic reaction-diffusion lattice systems defined on the entire set with both locally Lipschitz nonlinear drift and diffusion terms. The central limit theorem is derived for such infinite-dimensional stochastic systems. Moreover, the moderate deviation principle of solution processes is also established by the weak convergence method based on the variational representation of positive functionals of Brownian motion. The method relies on proving the convergence of the solutions of the controlled stochastic lattice systems.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582288","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}