Exact Results for First-Passage-Time Statistics in Biased Quenched Trap Models

Takuma Akimoto, Keiji Saito

Published 2019-01-03Version 1

We provide exact results for the mean and variance of first-passage times (FPTs) in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period $L$. FPT statistics are crucially affected by the disorder realization. In the large-$L$ limit, we obtain exact formulae for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulae are valid for nonperiodic heterogeneous environments, i.e, infinite systems. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.