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.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.

arXiv:math-ph/0511026Nov 7, 20050 citations

Repeated Interaction Quantum Systems

Laurent Bruneau

We consider a quantum system S interacting sequentially with independent systems Em, m = 1, 2,... Before interacting, each Em is in a possibly random state, and each interaction is characterized by an interaction time and an interaction operator, both possibly random. We prove that any initial state converges to an asymptotic state almost surely in the ergodic mean, provided the couplings satisfy a mild effectiveness condition. We analyze the macroscopic properties of the asymptotic state and show that it satisfies a second law of thermodynamics. We solve exactly a model in which S and all the Em are spins: we find the exact asymptotic state, in case the interaction time, the temperature, and the excitation energies of the Em vary randomly. We analyze a model in which S is a spin and the Em are thermal fermion baths and obtain the asymptotic state by rigorous perturbation theory, for random interaction times varying slightly around a fixed mean, and for small values of a coupling constant. 1We consider a quantum system S interacting sequentially with independent systems Em, m = 1, 2,... Before interacting, each Em is in a possibly random state, and each interaction is characterized by an interaction time and an interaction operator, both possibly random. We prove that any initial state converges to an asymptotic state almost surely in the ergodic mean, provided the couplings satisfy a mild effectiveness condition. We analyze the macroscopic properties of the asymptotic state and show that it satisfies a second law of thermodynamics. We solve exactly a model in which S and all the Em are spins: we find the exact asymptotic state, in case the interaction time, the temperature, and the excitation energies of the Em vary randomly. We analyze a model in which S is a spin and the Em are thermal fermion baths and obtain the asymptotic state by rigorous perturbation theory, for random interaction times varying slightly around a fixed mean, and for small values of a coupling constant. 1

Jan 1, 20070 citations

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.