Directed diffusion in a percolation network

Abstract

The authors investigate diffusion of particles in a random medium in the presence of an external field. The medium is modelled by a percolation network on which the particle executes a random walk with unequal transition probabilities along and against the biasing field. In one dimension where there are only finite clusters, they study how the bias affects the long-time approach to the steady state. In higher dimensions, they study the current-carrying steady state above the percolation threshold. They show that the drift velocity is non-monotonic and vanishes for large enough values of the field.