Kinetic Limit for Wave Propagation in a Random Medium

Details Kinetic Limit for Wave Propagation in a Random Medium Kinetic Limit for Wave Propagation in a Random Medium

2005-05-27

arxiv.org/abs/math-ph/0505075v1

Arch. Ration. Mech. Anal. 181 (2007) 93-162

Physics

Mathematical Physics

71 pages, 3 figures

Scientific paper

10.1007/s00205-006-0005-9

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.

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