Effective medium theory of A.C. Hopping conductivity for random-bond lattice models

We apply standard effective medium techniques to calculate the A.C. hopping conductivity of a system where the sites are located on a regular lattice but the intersite hop-rate is a random variable. The method is a generalization of Kirkpatrick's treatment of the D.C. conductivity of such a system. The results are compared with exact solution of the one-dimensional bond percolation problem and good agreement is found.