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 examples corresponding to realistic open quantum systems.
Highlights
A major challenge when investigating small quantum systems is to assess their dynamics when coupled to several environments that put the system in an out-of-equilibrium situation
We demonstrate the relevance of our perturbative analysis to assess the dynamics of realistic multipartite quantum systems characterized by Hilbert spaces of dimension as high as 8
We prove uniqueness of an invariant steady state under the coupled dynamics, analytic in the coupling constant, and provide a description of the converging power series of this non-equilibrium steady state that develops in the small system
Summary
A major challenge when investigating small quantum systems is to assess their dynamics when coupled to several environments that put the system in an out-of-equilibrium situation. One often resorts to effective master equations governing the reduced density operator for the small system. Under the Born-Markov approximation (that involves weak system-bath coupling and short bath time-correlations), the evolution equation for the reduced density operator becomes linear, and is cast into the form of a Lindblad-type master equation [12,13] for the corresponding map to be CPTP (Completely Positive and Trace Preserving). A Hamiltonian approach using perturbation theory is probably the most standard way to derive such a (continuous in time) effective evolution equation for the reduced quantum system [5,28].
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