Repeated interactions in open quantum systems

TL;DR

This paper studies the dynamics of open quantum systems through repeated interactions, providing insights into non-equilibrium behavior, decoherence, and entanglement, with applications in quantum optics and statistical mechanics.

Contribution

It introduces and analyzes repeated interaction models as a tractable approach to understanding non-equilibrium quantum dynamics and their long-term behavior.

Findings

Determines large time asymptotics of quantum systems out of equilibrium

Provides a framework for analyzing decoherence and entanglement dynamics

Connects quantum optical models with mathematical physics approaches

Abstract

Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.