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.

Plenary talk at QMath 10, Moeciu, Romania, September 10-15, 2007