The Linear Boltzmann Equation as the Low Density Limit of a Random   Schrodinger Equation
  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. 
David Eng and Laszlo Erdos