Exact closed master equation for Gaussian non-Markovian dynamics

TL;DR

This paper derives an exact closed-form master equation for Gaussian non-Markovian quantum dynamics, enabling comprehensive analysis of diverse open quantum systems without approximations.

Contribution

It provides the first exact closed master equation for Gaussian non-Markovian dynamics, unifying various physical models including quantum Brownian motion.

Findings

Master equation for non-Markovian quantum Brownian motion derived as a special case

Unraveled the master equation via a non-Markovian stochastic Schrödinger equation

Facilitates analysis of dissipative non-Markovian collapse models

Abstract

Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schr\"odinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.