ANALYSIS SEMINAR
Title: Exponential Ergodicity in Certain Quantum Markov Semigroups
Speaker:Zheng Li (Politecnico di Milano)
Time: Wednesday, March27, 2024, 16:00-17:30
Zoom ID: 946 1307 0421, Password: 371188
Abstract: 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.
More information about the Analysis Seminar can be found here.
