Kinetic Limit for Wave Propagation in a Random Medium

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.

71 pages, 3 figures

References in corpus (4)

• Self-averaging of Wigner transforms in random media
• Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field
• Radiative Transport in a Periodic Structure
• The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation

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