Diffusive limit for a quantum linear Boltzmann dynamics

Details Diffusive limit for a quantum linear Boltzmann dynamics Diffusive limit for a quantum linear Boltzmann dynamics

2010-11-10

arxiv.org/abs/1011.2439v2

Physics

Mathematical Physics

51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.1

Scientific paper

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.

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