The Boltzmann equation for a one-dimensional quantum lorentz gas

We study the macroscopic behavior of a quantum particle under the action of randomly distributed scatterers on the real line. Each scatterer generates a delta-potential. We prove that, in the low density limit, the Wigner fun ction of the system converges to a probability distribution satisfying a cl assical linear Boltzmann equation, with a scattering cross section computed according to the Quantum Mechanical rules.