Diffusion in a random medium: A renormalization group approach

Abstract

We investigate through a continuous random diffusion equation the long-distance properties of the general non-symmetric hopping model. The lower and upper critical dimensionalities are d = 1 and d = 2 respectively. A renormalization group analysis shows that the velocity and the diffusion constant obey scaling laws with non-classical exponents, which are computed to first order in ε = 2 − d. Similar scaling laws, based on heuristic arguments, are conjectured for the AC conductivity.