The linear Boltzmann equation as the low density limit of a random Schrödinger equation - Eng, David; Erdös, László (Reviews in Mathematical Physics, 2005)
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 by the full quantum scattering cross-section of the obstacle potential.
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