分析学研讨班
题目：Exponential Ergodicity in Certain Quantum Markov Semigroups
报告人：李政 (米兰理工大学)
时间：2024年3月27日（星期三），16:00-17:30
Zoom会议，会议号：946 1307 0421，密码：371188
摘要：Quantum Markov semigroups play a crucial role in characterizing the dynamics of open quantum systems. In this presentation, we explore the ergodic properties of quantum Markov semigroups possessing a faithful normal invariant state, along with an induced generator exhibiting a spectral gap. We demonstrate the exponential convergence of all normal states in a dense subset to some normal invariant state, with the rate of convergence determined by the spectral gap. Furthermore, we analyze the quantum Ornstein-Uhlenbeck semigroups when restricted to the diagonal subalgebra of the number operator. We highlight their non-uniform exponential convergence and identify a normal state that deviates from exponential convergence concerning the rate provided by the spectral gap. Additionally, we discuss an application of these findings to the quantum annealing problem.
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