Perturbation Analysis of Quantum Reset Models

TL;DR

This paper analyzes the dynamics of quantum reset models with stochastic resets in a tripartite system, proving the existence of a unique steady state and examining the approach to equilibrium.

Contribution

It introduces a rigorous analysis of Lindblad operators in quantum reset models, establishing conditions for unique steady states and their analytic dependence on coupling parameters.

Findings

Existence of a unique steady state under generic conditions.

Analytic dependence of the steady state on the coupling constant.

Concrete examples illustrating the theoretical results.

Abstract

This paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete exemples corresponding to realistic open quantum systems.