Linear Boltzmann equation as scaling limit of quantum Lorentz gas
We study a quantum particle in a random potential in two scaling limits: the low density limit (or Boltzman-Grad) and the weak coupling limit. The low density limit is the quantum analogue of the Lorentz gas. In both cases, the phase space density of the quantum evolution defined through the Wigner transform or the Husimi function converges weakly to a linear Boltz-mann equation with collision kernel given by the quantum scattering cross section.
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137 - 155
137 - 155
American Mathematical Society