Repeated Interaction Quantum Systems: Deterministic and Random

TL;DR

This paper reviews recent advances in understanding the long-term behavior of repeated interaction quantum systems, focusing on deterministic and random models, their steady states, thermodynamic implications, and the analysis of related random matrices.

Contribution

It provides a comprehensive overview of the dynamics, steady states, and thermodynamic laws in repeated interaction quantum systems, including the role of random matrix products.

Findings

Identification of non-equilibrium steady states in quantum systems

Derivation of a second law of thermodynamics for these systems

Analysis of random matrix products underlying the dynamics

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.