Repeated Interaction Quantum Systems: Deterministic and Random

Abstract

This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and we present, as a macroscopic consequence, a second law of thermodynamics these NESS give rise to. We also explain in some details the analysis of products of certain random matrices underlying this dynamical problem.