Exact Solution of a Boundary Value Problem in Semiconductor Kinetic Theory
Statistical Mechanics
2025-09-08 v1
Abstract
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be separable, which is also known as "relaxation time approximation"; the relaxation time may depend on the electron velocity. Our method consists in a transformation of the half-space problem into a nonnormal singular integral equation, which has an explicit solution.
Keywords
Cite
@article{arxiv.cond-mat/9702092,
title = {Exact Solution of a Boundary Value Problem in Semiconductor Kinetic Theory},
author = {C. Dalitz and E. H. de Groot},
journal= {arXiv preprint arXiv:cond-mat/9702092},
year = {2025}
}
Comments
19 pages in LaTex, figures omitted, submitted to J. Math. Phys