Effective medium theory of hopping transport

An effective medium theory for the calculation of the conductivity in the presence of inelastic scattering has been developed. Our approach turns out to be quite universal and applicable to arbitrary types of disorder. In contrast to other effective medium theories, our method does not rely on the introduction of an ordered lattice but focuses on the diffusion processes in the disordered media. We obtain a quantum diffusion equation in the presence of inelastic scattering which takes into account the Fermi correlation. The form of this equation shows the inapplicability of the concept of a spectral density for the conductivity used in earlier effective medium treatments. Furthermore, we apply our formalism to the calculation of the conductivity in the variable range hopping regime. For the de conductivity we obtain Mott's law. In addition, we derive a simple formula for the frequency dependence of the ac conductivity.