A Survey on Invariance and Ergodicity of Quantum Markov Semigroups

Abstract

This article surveys recent results on invariances and ergodicity of general quantum Markov semigroups of bounded linear maps acting on C*- or von Neumann algebra . In particular, we consider existence and uniqueness of invariant (stationary) quantum states as well as ergodicity and mean ergodicity of quantum states via heavy usage of the GNS representation. This survey is made self-contained by also reviewing relevant concepts and results necessary for the subsequent developments.