  We study the macroscopic transport properties of the quantum Lorentz gas in a
crystal with short-range potentials, and show that in the Boltzmann-Grad limit
the quantum dynamics converges to a random flight process which is not
compatible with the linear Boltzmann equation. Our derivation relies on a
natural hypothesis concerning the statistical distribution of lattice points in
thin domains, which is closely related to the Berry-Tabor conjecture in quantum
chaos.
