  In this article, I study the diffusive behavior for a quantum test particle
interacting with a dilute background gas. The model I begin with is a reduced
picture for the test particle dynamics given by a quantum linear Boltzmann
equation in which the gas particle scattering is assumed to occur through a
hard-sphere interaction. The state of the particle is represented by a density
matrix that evolves according to a translation-covariant Lindblad equation. The
main result is a proof that the particle's position distribution converges to a
Gaussian under diffusive rescaling.
