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.

本文致力于分析量子重置模型的 Lindblad 算子，描述受随机重置影响的三方量子系统的有效动力学。我们考虑由三个独立子系统组成的链，由哈密顿项耦合。链两端的两个子系统相互独立地由重置的 Lindbladian 驱动，而中心系统由哈密顿量驱动。在耦合项的一般假设下，我们证明了扰动重置 Lindbladian 的独特稳态的存在，在耦合常数中解析。我们进一步分析了描述稳态方法的相应 CPTP 马尔可夫半群的大时间动力学。我们用与现实开放量子系统相对应的具体例子来说明这些结果。