Abstract
A Master equation for the density matrix and a Boltzmann equation for the occupation number of electrons in a crystal are derived. The wave function of an electron is localized within a sub crystal by a superposition of the corresponding Wannier functions. The electrons are coupled to an external electrical field, to phonons, and to a particle reservoir, describing phenomena as transport, damping, and electron sources on the surface of contact.
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The author wants to thank to Prof. W. Weidlich and his coworkers for many stimulating discussions. Moreover the author is very indepted to Mr. K. Kaufmann and to Dr. K. Clausecker for their help preparing this paper.
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Gnutzmann, U. Master equation for the density matrix and Boltzmann equation of localized electrons in crystals. Z. Physik 243, 274–288 (1971). https://doi.org/10.1007/BF01394857
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DOI: https://doi.org/10.1007/BF01394857