Diffusive limit for a quantum linear Boltzmann dynamics
Mathematical Physics
2017-08-23 v2 math.MP
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.
Cite
@article{arxiv.1011.2439,
title = {Diffusive limit for a quantum linear Boltzmann dynamics},
author = {Jeremy Clark},
journal= {arXiv preprint arXiv:1011.2439},
year = {2017}
}
Comments
51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.1