The problem of the hopping conductivity of a system with randomly distributed impurity centers at low temperatures is considered on the basis of a linearized balance equation. Diagram techniques are used to find a self-consistent expression for the configuration-averaged Green's function describing charge transport in a disordered system with Fermi correlations taken into account. It is shown that the approximation chosen corresponds to the well-known coherent potential approximation. An expression for the hopping conductivity as a function of temperature and frequency for a power-law density of states is found in the low-frequency limit. The results are in good agreement with the percolation approach and, in the static limit, lead to Mott's law.
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