The Boltzmann equation as limit of a Schrödinger equation with random potential

Abstract

We study the transport of particles in time‐dependent random media in the so‐called weak coupling limit. We show how a limiting irreversible dynamic of Boltzmann's type can be derived from a reversible dynamic of Schrödinger's type. The homogenization is performed at the level of Wigner transforms for a mixed states formulation. We obtain a simple modelization of the influence of microscopic chaos on physical observables by means of a space–time Fourier transform of a covariance associated with the random variations.