A Boltzmann equation approach to transport in finite modular quantum systems

Kadiroglu, Mehmet; Gemmer, Jochen

doi:10.1140/epjst/e2007-00368-3

Cited by 1 publication

(1 citation statement)

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“…Finally, we note that a large number of works can be found in the literature which are related to the present subject. While it is impossible to do justice to all authors, we mention a few recent articles related to the derivation of a quantum kinetic equation in the spirit of the Boltzmann equation, both linear [70,71,72,73,74,75,76,77,78,79,80] and nonlinear [11,12,13,14,15,16,17,20,81,82,83,23,84,85].…”

Section: Survey and Comparison Of Derivations In The Literaturementioning

confidence: 99%

Quantum linear Boltzmann equation

2009

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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.Comment: 63 pages, 6 figures; v3:corresponds to published versio

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