标题： 量子马尔可夫半群的遍历性质 显示英文标题

标题： Ergodic Properties of Quantum Markov Semigroups

摘要： 在本文中，我们研究了无限维量子马尔可夫半群的遍历定理，该定理最初由Frigerio和Verri于1982年提出，并由Carbone和Girotti于2021年开发了最新版本。我们提供了一个充分条件，确保指数收敛到正遍历子空间，这是有限维希尔伯特空间中不可约量子马尔可夫半群的一个著名结果。给出了几个示例来展示遍历定理的应用。此外，我们表明正遍历子空间在全局渐近稳定性研究中起着关键作用。 显示英文摘要

摘要： In this paper, we study the ergodic theorem for infinite-dimensional quantum Markov semigroups, originally introduced by Frigerio and Verri in 1982, and its latest version developed by Carbone and Girotti in 2021. We provide a sufficient condition that ensures exponential convergence towards the positive recurrent subspace, a well-known result for irreducible quantum Markov semigroups in finite-dimensional Hilbert spaces. Several illustrative examples are presented to demonstrate the application of the ergodic theorem. Moreover, we show that the positive recurrent subspace plays a crucial role in the study of global asymptotic stability.