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THE LINEAR BOLTZMANN EQUATION AS THE LOW DENSITY LIMIT OF A RANDOM SCHRĂ–DINGER EQUATION
We study the long time evolution of a quantum particle interacting with a random potential in the Boltzmann–Grad low density limit. We prove that the phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation. The Boltzmann collision kernel is given …