Quantum linear Boltzmann equation

Details Quantum linear Boltzmann equation Quantum linear Boltzmann equation

2009-04-24

arxiv.org/abs/0904.3911v3

Physics Reports 478 (2009) 71-120

Physics

Quantum Physics

63 pages, 6 figures; v3:corresponds to published version

Scientific paper

10.1016/j.physrep.2009.06.001

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

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