Time-Periodic Behaviour in One- and Two-Dimensional Interacting Particle Systems

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2025-09-17 DOI:10.1007/s00023-025-01624-5

Benedikt Jahnel, Jonas Köppl

引用次数: 0

Abstract

We provide a class of examples of interacting particle systems on \(\mathbb {Z}^d\), for \(d\in \{1,2\}\), that admit a unique translation-invariant stationary measure, which is not the long-time limit of all translation-invariant starting measures, due to the existence of time-periodic orbits in the associated measure-valued dynamics. This is the first such example and shows that even in low dimensions, not every limit point of the measure-valued dynamics needs to be a time-stationary measure.

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一维和二维相互作用粒子系统的时间周期行为

我们在\(\mathbb {Z}^d\)上提供了一类相互作用粒子系统的例子，对于\(d\in \{1,2\}\)，由于在相关的测量值动力学中存在时间周期轨道，它允许唯一的平移不变平稳测度，而不是所有平移不变起始测度的长时间极限。这是第一个这样的例子，并表明即使在低维中，并非每个测量值动力学的极限点都需要是时间平稳的测量。

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

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.