Diffusion Coefficients of Single and Many Particles in Lattices with Different Forms of Disorder

TL;DR

This paper reviews and discusses various exact and approximate methods for calculating diffusion coefficients of particles in disordered lattices, highlighting recent exact results and their applications to different models.

Contribution

It provides a comprehensive survey of diffusion coefficients in disordered lattices, including new exact expressions in one dimension and their application to multiple models.

Findings

Exact expression for 1D diffusion including occupation factors

Application of results to Miller-Abrahams model

Results for site-exclusion models in disordered lattices

Abstract

A survey is given on asymptotic diffusion coefficients of particles in lattices with random transition rates. Exact and approximate results for single particles are reviewed. A recent exact expression in $d = 1$ which includes occupation factors is discussed. The utilization of the result is demonstrated for the Miller-Abrahams model and a model of random barriers combined with random traps. Exact and approximate results for the site-exclusion model in disordered lattices are also given.