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arXiv:1512.07244 · Physical Review Letters

Exact Closed Master Equation for Gaussian Non-Markovian Dynamics

Luca Ferialdi

Published Mar 22, 2016• 80 citations
arXivHTMLPDF

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 us 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 Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.

DOI
10.1103/physrevlett.116.120402

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We construct a large class of completely positive and trace-preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics for statistical operators characterized by a continuous time evolution interrupted by jumps, randomly distributed in time and described by a quantum channel. The state of the open system is shown to obey a closed evolution equation, given by a master equation with a memory kernel and an inhomogeneous term. The non-Markovianity of the obtained dynamics is explicitly assessed studying the behavior of the distinguishability of two different initial system's states with elapsing time.