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

## TL;DR

This paper derives exact formulas for the mean and variance of first-passage times in biased quenched trap models, providing insights into diffusion in heterogeneous environments with disorder.

## Contribution

It presents the first exact analytical results for FPT statistics in biased quenched trap models, applicable to large systems and nearly all disorder realizations.

## Key findings

- Exact formulas for FPT mean and variance in large systems
- Results applicable to nonperiodic heterogeneous environments
- Provides a basis for estimating diffusivity in disordered media

## Abstract

We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution 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 still useful for nonperiodic heterogeneous environments; i.e, the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.