Establishment of a transport equation in a system of localised electron states

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Abstract
The model of Miller and Abrahams (1960) describes the effective conductivity in a system of localised electronic states as a thermally stimulated hopping conductivity between the sites. Using Liouville's theorem and applying the method of Argyres and Sigel (1974) to the physical processes involved, the author has derived a system of Boltzmann-type equations for the average occupation of the electronic states. Until now, the treatment of this transport problem with a Boltzmann formalism was only justified phenomenologically. The electrical equivalence scheme of hopping conduction already proposed by Pollak (1974) is confirmed and an improved expression for the conductance of the pairs used in the Miller and Abraham's network is given.