Diffusion in the presence of quenched random bias fields: A two-dimensional generalization of the Sinai model

We report a theoretical and numerical study of diffusion in two dimensions in the presence of quenched random bias fields. The local bias field is taken to be the gradient of a random scalar potential V(i,j). We consider the special case V(i,j)=V₁(i)+V₂(j), where the gradients of V₁ and V₂ are chosen to be randomly ±{}ε₀ with 0ε₀{≤}1. We find that asymptotically (t{→}{∞}) the mean square displacement grows with the time t as (lnt)⁴, just as in the one-dimensional Sinai model.