Kinetic Limit for Wave Propagation in a Random Medium

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 √ ε. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit ε → 0 the disorder averaged Wigner function on the kinetic scale, time and space of order ε, is governed by a linear Boltzmann equation.