Mean field dynamics of some open quantum systems

TL;DR

This paper develops an expansion method for analyzing the dynamics of large quantum systems coupled to a reservoir, providing insights into their behavior in the mean field limit.

Contribution

It introduces an inverse square root N expansion for observable averages in open quantum systems with mean field interactions, based on Dyson series analysis.

Findings

Derivation of an expansion for observable averages in the large N limit.

Application to the infinite mode Dicke model and energy conserving models.

Insights into the dynamics and fluctuations of quantum particles and reservoirs.

Abstract

We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of $\sqrt{N}$. The analysis is based directly on the Dyson series expansion of the propagator. We analyze the dynamics, in the limit $N\rightarrow\infty$, of observables of a fixed number $n$ of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy conserving models.