Time evolution of open quantum many-body systems

TL;DR

This paper introduces a variational method to analyze the time evolution of open quantum many-body systems, effectively capturing non-Markovian effects and accurately modeling dissipative Rydberg gases.

Contribution

The authors develop a novel variational approach for the quantum master equation, linking dynamics and steady states, and demonstrate its effectiveness on dissipative Rydberg gases.

Findings

Excellent agreement with full quantum simulations

Non-Markovian correlations significantly influence relaxation dynamics

Quantified non-Markovianity linked to quantum and classical correlations

Abstract

We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding excellent quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics towards the steady state. We further quantify this non-Markovianity and find it to be closely connected to an information-theoretical measure of quantum and classical correlations.