Quantum dynamics with non-Markovian fluctuating parameters

TL;DR

This paper develops an exact stochastic framework for quantum dynamics influenced by non-Markovian noise with arbitrary residence time distributions, generalizing existing theories and applying to spectral line shape analysis.

Contribution

It introduces a formally exact expression for quantum propagators under non-Markovian noise, extending the Kubo-Anderson theory to non-Markovian regimes.

Findings

Derived an exact analytical spectral line shape for non-Markovian frequency fluctuations.

Unified Markovian and non-Markovian cases within a single theoretical framework.

Applicable to quantum systems with complex noise characteristics.

Abstract

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.