Ergodic and Non-Ergodic Phenomena in One-Dimensional Random Processes: Exploring Unconventional State Transitions

IF 1.3 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
A. D. Ramos, C. S. Sousa, L. P. Cavalcanti
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引用次数: 0

Abstract

Traditionally, the evolution of interacting particle systems has been based on an assumption that only the individual components undergo state changes. However, this rigid assumption is not the only possibility. This research explored a class of one-dimensional random processes that evolved in discrete time. During each time step, components in the state zero exhibited the following transitions. First, they could change to one with a probability \(\beta _0\). Second, they could be replaced by a sequence of k consecutive zeros with a probability \(\beta _k\) (where \(k=1,\ldots ,n\)). Moreover, these transitions occurred independent of the events occurring elsewhere in the involved system. Notably, this study revealed an unexpected phenomenon—the occurrence of a first-order phase transition between ergodic and non-ergodic behaviors within this system. Furthermore, in the non-ergodic regime, the existence of an invariant measure distinct from the trivial one was demonstrated.

Abstract Image

一维随机过程中的遍历与非遍历现象:探索非常规状态转换
传统上,相互作用的粒子系统的演化是基于一个假设,即只有单个组分经历状态变化。然而,这种刻板的假设并不是唯一的可能性。本研究探讨了一类在离散时间演化的一维随机过程。在每个时间步长期间,处于零状态的分量表现出以下转变。首先,它们可以以\(\beta _0\)的概率变为1。其次,它们可以被概率为\(\beta _k\)(其中\(k=1,\ldots ,n\))的k个连续零序列所取代。此外,这些转变的发生与相关系统中其他地方发生的事件无关。值得注意的是,本研究揭示了一个意想不到的现象——在该系统的遍历和非遍历行为之间发生了一阶相变。此外,在非遍历状态下,证明了不同于平凡测度的不变测度的存在性。
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来源期刊
Annales Henri Poincaré
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.
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