Non-Markovian dynamics of quantum systems. I. Formalism and transport coefficients

Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of general and linear couplings in the coordinate and momen...

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Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2005-01, Vol.71 (1 Pt 2), p.016121-016121, Article 016121
Main Authors: Kanokov, Z, Palchikov, Yu V, Adamian, G G, Antonenko, N V, Scheid, W
Format: Article
Language:English
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Summary:Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of general and linear couplings in the coordinate and momentum between the collective harmonic oscillator and heat bath. The long-time tails of correlation functions are investigated in the low- and high-temperature regimes of dissipation for different couplings. The Onsager's regression hypothesis is discussed for the non-Markovian dynamics. The Lindblad theory is justified on the basis of the microscopical model.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.71.016121