Diffusive Limit for a Quantum Linear Boltzmann Dynamics

In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model that 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.