Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application

TL;DR

This paper develops a mean-field framework for open quantum many-body systems with collective, state-dependent dissipation, demonstrating the exactness of mean-field equations in the large-system limit and exploring quantum effects on classical models.

Contribution

It introduces a rigorous mean-field approach for a class of open quantum systems with collective rates, extending classical stochastic models to the quantum domain.

Findings

Mean-field equations are exact in the infinite system limit.

Derived effective generators for local operator dynamics.

Applied framework to quantum models like Hopfield memories.

Abstract

We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ``state-dependent" rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-)local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models.