We consider a sequence of operators ${\tau }_n$ that describes the time evolution of normal states of an open quantum system. Our objective is to analyze the asymptotic behavior of ${\tau }_n\circ \cdots \circ {\tau }_1({\omega }_0)$, where ${\omega }_0$ is an arbitrary initial normal state. Our focus is on specific situations in which the operators ${\tau }_n$ are produced by various quantum Markov semigroups of weak coupling limit-type. To tackle this problem, we introduce a new result concerning exponential convergence to equilibrium in the trace norm for quantum Markov semigroups, provided that their induced semigroups have a spectral gap. Moreover, applications to quantum annealing are discussed.

中文翻译：

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迹范数的指数收敛和 ℬ(ℋ) 上的时间非齐次马尔可夫演化

我们考虑一系列运算符${\tau }_n$它描述了开放量子系统正常状态的时间演化。我们的目标是分析渐近行为${\tau }_n\circ \cdots \circ {\tau }_1（{\omega }_0）$， 在哪里${\omega }_0$是任意初始正常状态。我们的重点是运营商的特定情况${\tau }_n$由弱耦合极限型的各种量子马尔可夫半群产生。为了解决这个问题，我们引入了一个关于量子马尔可夫半群的迹范数指数收敛到平衡的新结果，前提是它们的诱导半群具有谱间隙。此外，还讨论了量子退火的应用。