Non-Markovian stochastic Liouville equation and anomalous relaxation kinetics

TL;DR

This paper analyzes anomalous relaxation kinetics in quantum systems affected by noise with slowly decaying correlations, revealing slow, alpha-dependent relaxation behaviors and transitions from static to fluctuation narrowing regimes.

Contribution

It introduces a non-Markovian stochastic Liouville framework for anomalous relaxation, providing analytical expressions and insights into the transition regimes as correlation decay exponent approaches one.

Findings

Relaxation is anomalously slow for 0<alpha<1.

Kinetics becomes independent of fluctuation rate as alpha approaches 1.

Transition from static to fluctuation narrowing regimes occurs at alpha close to 1.

Abstract

The kinetics of phase and population relaxation in quantum systems induced by noise with anomalously slowly decaying correlation function P (t) ~ (wt)^{- alpha}, where 0 < alpha < 1 is analyzed within continuous time random walk approach. The relaxation kinetics is shown to be anomalously slow. Moreover for alpha < 1 in the limit of short characteristic time of fluctuations w^{-1} the kinetics is independent of w. As alpha \to 1 the relaxation regime changes from the static limit to fluctuation narrowing. Simple analytical expressions are obtained describing the specific features of the kinetics.