Finite Size Effect in Persistence

TL;DR

This paper investigates how finite system size affects the persistence probability in random walk problems, revealing that the scaling function decays exponentially in various trapping scenarios through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of finite size effects on persistence, including trapped particles and accelerated particles, with new insights into the exponential decay of the scaling function.

Findings

Scaling function decays exponentially with system size.

Finite size induces a crossover in persistence probability.

Numerical and analytical results agree on exponential decay.

Abstract

We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially decaying function.The particle here is trapped with in a box of size $L$ . We have also considered the problem when the particle in trapped in a potential. Direct calculation and numerical result show that the scaling function here also an exponentially decaying function. We also present numerical works on harmonically trapped randomly accelerated particle and randomly accelerated particle with viscous drag.