Diffusive limit for a quantum linear Boltzmann dynamics
arXiv:1011.2439 · doi:10.1007/s00023-012-0223-7
Abstract
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.
51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.1