Combination of random-barrier and random-trap models

TL;DR

This paper investigates how combined trap and barrier disorder affect particle diffusion in lattices, using effective-medium approximation and simulations to understand Arrhenian temperature dependence.

Contribution

It introduces a generalized EMA for mixed disorder models and analyzes conditions for Arrhenian behavior in various dimensions.

Findings

Arrhenian behavior achievable in finite dimensions with parameter tuning

Exact Arrhenian behavior only in infinite dimensions

Monte Carlo simulations validate the EMA approximation

Abstract

The temperature dependence of the diffusion coefficient of particles is studied on lattices with disorder. A model is investigated with both trap and barrier disorder that was introduced before by Limoge and Bocquet (1990 Phys. Rev. Lett. (65) 60) to explain an Arrhenian temperature-dependence of the diffusion coefficient in amorphous substances. We have used a generalized effective-medium approximation (EMA) by introducing weighted transition rates as inferred from an exact expression for the diffusion coefficient in one-dimensional disordered chains. Monte Carlo simulations were made to check the validity of the approximations. Approximate Arrhenian behavior can be achieved in finite temperature intervals in three- and higher-dimensional lattices by adjusting the relative strengths of the barrier and trap disorder. Exact Arrhenian behavior of the diffusion coefficient can only be obtained in infinite dimensions.