A numerical study of diffusion and conduction in a 2D random medium

Abstract

Investigates numerically the diffusion and conduction properties of a two-dimensional random lattice hopping model. The results are compared with a recent field theoretical renormalisation group approach, showing that two is the upper critical dimension for such models. The predicted scaling law with a universal logarithmic behaviour of the velocity is clearly observed. The finiteness of the diffusion constant are well as its regular dependence versus the strength of randomness are evenly in good agreement with analytical results. The author also determines the frequency dependence of the AC conductivity tensor.