  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.
