Asymptotics of repeated interaction quantum systems

TL;DR

This paper analyzes the long-term behavior of a quantum system repeatedly interacting with a chain of identical subsystems, showing convergence to a periodic asymptotic state and deriving thermodynamic properties.

Contribution

It establishes the asymptotic state of repeated quantum interactions and links it to thermodynamic laws, extending understanding of quantum system dynamics.

Findings

System approaches a time-periodic asymptotic state

Asymptotic state is independent of initial conditions

Satisfies an average second law of thermodynamics

Abstract

A quantum system $\s$ interacts in a successive way with elements $\ee$ of a chain of identical independent quantum subsystems. Each interaction lasts for a duration $\tau$ and is governed by a fixed coupling between $\s$ and $\ee$. We show that the system, initially in any state close to a reference state, approaches a {\it repeated interaction asymptotic state} in the limit of large times. This state is $\tau$--periodic in time and does not depend on the initial state. If the reference state is chosen so that $\s$ and $\ee$ are individually in equilibrium at positive temperatures, then the repeated interaction asymptotic state satisfies an average second law of thermodynamics.