The strong-coupling master equation of quantum open systems

TL;DR

This paper develops a new class of non-Markovian strong-coupling master equations for quantum open systems with continuous variables, expanding understanding beyond traditional weak-coupling and Markovian approximations.

Contribution

It introduces a novel framework for deriving non-Markovian master equations applicable in strong noise and dissipation regimes, differing from existing perturbative approaches.

Findings

Derivation of non-Markovian master equations for strong coupling

Equations vary significantly with different system potentials

Applicable to environments with large 1/f fluctuations

Abstract

In this paper we demonstrate how to generate the strong-coupling master equations for open quantum systems of continuous variables. These are the dissipative master equations of quantum Brownian particles for which the environmental noise is stronger than other system forces. Our strong-coupling master equations are very different from other so-called "strong-coupling" master equations (e.g. the quantum Smoluchowski equation) which are perturbing off a limit in which the system energy is taken to be perturbative and thus the dynamics is principally Markovian. Such approximations also require the system mass to be asymptotically large (even as compared to the ratio of noise and induced system frequencies) and thus they do not fully categorize the regime of what one might consider to be strong coupling. Our master equations are highly non-Markovian and radically different for different system potentials, admitting no apparent generic form. This result is quite exciting as it brings forth a new regime for theoretical exploration: the regime of strong noise and dissipation yet non-Markovian, such as strong coupling to a low-temperature environment with large 1/f fluctuations.