Survival and residence times in disordered chains with bias

TL;DR

This paper develops a unified theoretical framework to analyze first-passage and residence times of biased random walks in disordered one-dimensional systems, considering various disorder strengths and initial conditions.

Contribution

It introduces an exact cumulant expansion approach for the backward master equation, providing new insights into time dynamics in disordered biased chains.

Findings

Explicit dependence on initial conditions, system size, and bias strength.

Application to thermally activated processes.

Framework applicable to both weak and strong disorder regimes.

Abstract

We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on exact expansion of the backward master equation in cumulants. The dependence on initial condition, system size, and bias strength is explicitly studied for models with weak and strong disorder. Application to thermally activated processes is also developed.