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Asymptotics of repeated interaction quantum systems

Laurent Bruneau·Alain Joye·Marco Merkli
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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 $τ$ 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 $τ$--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.

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Laurent Bruneau, Alain Joye, Marco Merkli. 2005-11-07. Asymptotics of repeated interaction quantum systems. https://arxiv.org/abs/math-ph/0511026

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