On the Mott formula for the ac conductivity and binary correlators in the strong localization regime of disordered systems

Abstract

We present a method that allows us to find asymptotic form of various characteristics of disordered systems in the strong localization regime, i.e., when either the random potential is big enough or the energy is close enough to the spectrum edges. The method is based on the hypothesis that relevant realizations of the random potential in the strong localization regime have the form of deep random wells that are uniformly and chaotically distributed in the space with a sufficiently small density. Assuming this and using the density expansion, we show first that the density of wells coincides in the leading order with the density of states. Thus the density of states is in fact the small parameter of the theory in the strong localization regime. Then we derive the Mott formula for the low frequency conductivity and the asymptotic formulas for certain two-point correlators when the difference of respective energies is small.