On a Heuristic Expansion Method in the Strong Localization Regime of the Theory of Disordered Systems

Abstract

We present a method that allows us to compute various spectral and physical characteristics of disordered systems in the strong localization regime, i.e. when either the random potential is big enough or if the energy is close enough to the spectrum edges. The method is based on the hypothesis that in the strong localization regime relevant realizations of the random potential have the form of deep potential wells that are uniformly and chaotically distributed in the space, can be parameterized by at least one continuously distributed parameter and have small density. Assuming this and using the density expansion and the analysis of the tunnelling in the system of several wells 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 the density-density correlation functions when the difference of energies is small.