Diffusion and drift on percolation networks in an external field

Abstract

The diffusion of a particle on a percolation network is studied in the presence of an external field which makes the particle more likely to move along the field than otherwise. It is shown that while in weak fields, less than a critical value, the mean displacement is linear in time; in the presence of strong fields, the particle has zero drift velocity but the mean displacement varies as t^alpha for large times t, where alpha is a non-universal field-dependent exponent less than one.