Persistence and First-Passage Properties in Non-equilibrium Systems

TL;DR

This review explores the persistence and first-passage properties in various non-equilibrium many-body systems, highlighting theoretical methods, generalizations, and experimental aspects of these complex stochastic processes.

Contribution

It provides a comprehensive overview of recent theoretical advances and methods for analyzing persistence in non-Markovian, many-body non-equilibrium systems, including generalizations and experimental considerations.

Findings

Development of exact and approximate methods for non-Markovian persistence

Analysis of persistence in systems with quenched disorder

Discussion of experimental systems related to persistence phenomena

Abstract

In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.