Mott variable range hopping

Abstract: We consider a random walk on a simple point process in R^d with energy marks. The jump rates decay by a A-power of the jump length (A>0) and depend on the energy marks via a Boltzmann-like factor. The case A=1 corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We discuss the diffusive/subdiffusive behavior of the random walk and, in the diffusive regime, we show estimates on the diffusion matrix in agreement with Mott law.