Kпеtiс equation for localized electrons in the field of а strong electromagnetic wave

We obtain a kinetic equation describing the low-frequency relaxation function of the occupation of localized states in the presence of both a constant electric field and a strong electromagnetic wave. By investigating the solutions of this equation using the ideas of flow theory, one can find the effect of a strong electromagnetic wave on the hopping conductivity in two cases: a) when the conductivity is due to hops along a narrow band of impurity centers which are randomly distributed in space, and b) when the energies of the localized states are continuously distributed over a wide interval. It is shown that in the first case the weakening of the effective electron-phonon interaction in the field of the wave leads to a negative photoconductivity, and in the second case there must be a specific exponential dependence of the hopping conductivity on the amplitude of the wave.