2003/11/30 by Igor Goychuk · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Context (archaeology) #Generalization #Laplace transform #Markov process #Mathematical analysis #Mathematics #Physics #Propagator #Quantum #Quantum Information and Cryptography #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.70.016109
published as Phys. Rev. E 70, 016109 (2004)
arxiv created 2004/05/17 · openalex publication_date 2004/07/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary nonexponential 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 the 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 jumplike non-Markovian fluctuations in time.