Hydrodynamical Behavior for the Symmetric Simple Partial Exclusion with Open Boundary

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2023-05-08 DOI:10.1007/s11040-023-09446-9

C. Franceschini, P. Gonçalves, B. Salvador

引用次数: 4

Abstract

We analyze the symmetric simple partial exclusion process, which allows at most \(\alpha \) particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter \(\theta \in {\mathbb {R}}\). We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of \(\theta \), the equation is supplemented with different boundary conditions. Setting \(\alpha = 1\) we find the results known in Baldasso et al. (J Stat Phys 167(5):1112–1142, 2017) and Bernardin et al. (Markov Processes Relat. Fields 25:217–274, 2017) for the symmetric simple exclusion process.

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开边界对称简单部分不相容的流体力学行为

我们分析了对称的简单部分不相容过程，该过程允许每个位点最多\(\alpha \)个粒子，并将其与随机储层接触，其强度由参数\(\theta \in {\mathbb {R}}\)调节。我们证明了水动力行为由热方程给出，并根据\(\theta \)的值，在方程中补充不同的边界条件。通过\(\alpha = 1\)我们可以找到Baldasso et al. (J Stat Phys 167(5): 1112-1142, 2017)和Bernardin et al. (Markov过程相关)中已知的结果。Fields 25:17 - 274, 2017)，用于对称简单排除过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.