A self-consistent approach to linear and nonlinear transport in an electric field

H. Moraal

Physica A: Statistical Mechanics and its Applications, 1982, vol. 113, issue 3, 417-440

Abstract: The Boltzmann equation for charge carriers (obeying any statistics) is solved analytically in terms of electric-field-dependent relaxation times for a model collision operator. This operator is a linear, rotationally invariant one, which reduces to a multiplicative operator in each irreducible tensor subspace. The relaxation times are given by a self-consistency requirement. This gives (i) an exact solution of the Boltzmann equation for energy-independent multiplicative factors and (ii) exact asymptotic solutions for low- and high-field situations. Ohm's law is shown to hold exactly in case (i). Furthermore, a number of simple models is shown to be exactly soluble. For more complicated cases, perturbative and iterative methods of solution are discussed.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:113:y:1982:i:3:p:417-440

DOI: 10.1016/0378-4371(82)90148-0

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