Kinetic Limit for Wave Propagation in a Random Medium
Mathematical Physics
2007-05-23 v1 Disordered Systems and Neural Networks
math.MP
Abstract
We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon to 0 the disorder averaged Wigner function on the kinetic scale, time and space of order epsilon^(-1), is governed by a linear Boltzmann equation.
Keywords
Cite
@article{arxiv.math-ph/0505075,
title = {Kinetic Limit for Wave Propagation in a Random Medium},
author = {Jani Lukkarinen and Herbert Spohn},
journal= {arXiv preprint arXiv:math-ph/0505075},
year = {2007}
}
Comments
71 pages, 3 figures