Hopping dynamics in random energy landscapes: an effective medium approach

An effective medium approximation is given for single-particle hopping in lattices with site energy disorder. Based on this approximation the frequency dependent diffusion coefficient is calculated for a uniform distribution of site energies and the results compared with Monte Carlo simulations. Although the approximation gives a fairly good account of the overall frequency dependence, generally it fails to reproduce the correct zero-frequency limit of the diffusion coefficient. This failure may be resolved by a proper rescaling of the temperature in the effective medium. Possible extensions of the theory are pointed out.