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Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most...

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Bibliographic Details
Main Authors: Souza Fraga, Eduardo (Author) , Krein, Gastão (Author) , Palhares, Leticia F. (Author)
Format: Article (Journal)
Language:English
Published: 2014
In: Physica. A, Statistical mechanics and its applications
Year: 2013, Volume: 393, Pages: 155-172
ISSN:1873-2119
DOI:10.1016/j.physa.2013.09.018
Online Access:Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.physa.2013.09.018
Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0378437113008492
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Author Notes:Eduardo S. Fraga, Gastão Krein, Letícia F. Palhares
Description
Summary:We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation–dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form.
Item Description:Available online 19 September 2013
Gesehen am 06.10.2020
Physical Description:Online Resource
ISSN:1873-2119
DOI:10.1016/j.physa.2013.09.018

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