Kinetic limit for wave propagation in a random medium

被引：64

作者：

Lukkarinen, Jani ^{[1
]}

Spohn, Herbert ^{[1
]}

机构：

[1] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2007年 / 183卷 / 01期

关键词：

LINEAR BOLTZMANN-EQUATION; RANDOM SCHRODINGER-EQUATION; WIGNER TRANSFORMS; TRANSPORT;

D O I：

10.1007/s00205-006-0005-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of the order root epsilon. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon -> 0, the disorder-averaged Wigner function on the kinetic scale, time and space of order epsilon(-1), is governed by a linear Boltzmann equation.

引用

页码：93 / 162

页数：70

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