The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation

Abstract

We study the evolution of a quantum particle interacting with a random potential in the low density limit (Boltzmann-Grad). The phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation with collision kernel given by the full quantum scattering cross section.

arXiv comment74 pages, 4 figures, (Final version -- typos corrected)

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