Application of Functional Integrals to the Study of Sundry Electronic Properties of Disordered Systems in the Strongly Localized Regime

We find the density of electronic energy levels in the low energy limit for d-dimensional disordered systems which consist of randomly distributed scattering centers with repulsive long range and with attractive scatterers. In addition we derive, in a very general context, the Mott result for low frequency a.c. conductivity, (sigma)((omega)), in disordered systems whose Fermi energy, (mu), is far below the mobility edge. If the frequency, (omega), is much less than (mu) then (sigma)((omega)) = A (omega)('2)(Ln c/(omega))('d+1) where A and c have been determined.