Abstract
We treat the problem of a single electron interacting only with the lattice vibrations of its host crystal with and without the application of a weak electric field. A Markovian solution which applies in the limit of a large number of collisions is given to the exact integro-differential equation for the electron's density matrix. This equation was derived earlier from the path-integral representation of Feynman et al. for a polaron. The solution, which corresponds to the observed phenomenological description, averages out memory effects. The Einstein diffusion relation is found to hold closely, and realistic results are obtained for the temperature dependence of the mobility and for the deformation-potential coupling constants of silicon and germanium.
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