Quantum dynamics with non-Markovian fluctuating parameters

Details Quantum dynamics with non-Markovian fluctuating parameters Quantum dynamics with non-Markovian fluctuating parameters

2003-11-26

arxiv.org/abs/cond-mat/0311596v3

Phys. Rev. E 70, 016109 (2004)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.70.016109

A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression for the Laplace-transformed quantum propagator averaged over the stationary realizations of such N-state non-Markovian noise is obtained. The theory possesses a wide range of applications. It includes some previous Markovian and non-Markovian theories as particular cases. In the context of stochastic theory of spectral line shape and relaxation, the developed approach presents a non-Markovian generalization of the Kubo-Anderson theory of sudden modulation. In particular, the exact analytical expression is derived for the spectral line shape of optical transitions described by a Kubo-oscillator with randomly modulated frequency which undergoes jump-like non-Markovian fluctuations in time.

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