Non-Markovian dynamics of quantum systems. I. Formalism and transport coefficients
Abstract
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.
- Publication:
-
Physical Review E
- Pub Date:
- January 2005
- DOI:
- 10.1103/PhysRevE.71.016121
- Bibcode:
- 2005PhRvE..71a6121K
- Keywords:
-
- 05.30.-d;
- 05.40.-a;
- 03.65.-w;
- 24.60.-k;
- Quantum statistical mechanics;
- Fluctuation phenomena random processes noise and Brownian motion;
- Quantum mechanics;
- Statistical theory and fluctuations