Sample-dependent first-passage time distribution in a disordered medium

TL;DR

This paper investigates how the distribution of first-passage times in disordered media varies across different samples, revealing significant sample-to-sample fluctuations and confirming theoretical predictions through numerical simulations.

Contribution

It introduces an approximate expression for the sample-specific FPT distribution, enabling comparison between quenched disorder and annealed CTRW models.

Findings

Existence of two characteristic time scales in FPT distribution

Sample-to-sample variations are significant due to trap configurations

Numerical simulations confirm non-self-averaging behavior of FPTs

Abstract

Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT) distribution in a given sample that enables detailed comparison of the two problems. For a system of finite size, the number and spatial arrangement of deep traps yield significant sample-to-sample variations in the FPT statistics. Numerical simulations of a quenched trap model with power-law sojourn times confirm the existence of two characteristic time scales and a non-self-averaging FPT distribution, as predicted by theory.