Energy space diffusion of hopping excitations in non-equilibrium

The effective medium theory of hopping by Bleibaum, Bottger and Bryksin is generalized to finite temperatures. Starting point is the system of rate equations for the (localized) site occupation numbers of a disordered system. An effective generalized Fokker-Planck equation is derived thereof, which contains terms describing diffusion in real space, as well as terms describing drift and diffusion in energy space. The corresponding effective medium is determined self-consistently. The theory describes the relaxation in a system of localized excitations, where transitions are possible by hopping. It considers the behavior at high temperatures, corresponding to nearest neighbor hopping.