Diffusion and percolation in anisotropic random barrier models

TL;DR

This paper investigates anisotropic random barrier models, revealing how directional differences affect diffusion and percolation, with theoretical predictions validated by numerical simulations.

Contribution

It introduces an effective medium approximation for anisotropic models, linking activation energy to percolation properties and accurately predicting percolation thresholds.

Findings

Activation energy is consistent across directions at low temperatures.

Effective medium approximation predicts percolation threshold accurately.

Numerical simulations confirm theoretical predictions.

Abstract

An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained using an effective medium approximation, follow an Arrhenius temperature dependence, with the same activation energy for each direction. Such activation energy is related to the anisotropic percolation properties of the lattice, and can be analysed in terms of the critical percolation path approximation. The anisotropic effective medium approximation is shown to predict the correct percolation threshold for an anisotropic two--dimensional square lattice. In addition, results are compared with numerical simulations using a fast kinetic Monte Carlo algorithm.