Effective-Medium Approximation for Diffusion on a Random Lattice

A self-consistent effective-medium approximation is presented for the problem of diffusion and ac conductivity on a lattice characterized by random values of transfer rates between pairs of nearest-neighbor sites. The approximation is applied to a percolation model in which only a fraction of the bonds are assigned a finite transfer rate. The results reflect the existence of a percolation threshold in the system, and are consistent with the properties of clusters of bonds in the critical region.