# Repeated interactions in open quantum systems

## 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.

- Authors:

- Laboratoire AGM, Université de Cergy-Pontoise, Site Saint-Martin, BP 222, 95302 Cergy-Pontoise (France)
- Institut Fourier, UMR 5582, CNRS-Université Grenoble I, BP 74, 38402 Saint-Martin d’Hères (France)
- Department of Mathematics and Statistics Memorial University of Newfoundland, St. John's, NL Canada A1C 5S7 (Canada)

- Publication Date:

- OSTI Identifier:
- 22306192

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; EQUILIBRIUM; OPTICS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; THERMODYNAMIC PROPERTIES

### Citation Formats

```
Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr, Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr, and Merkli, Marco, E-mail: merkli@mun.ca.
```*Repeated interactions in open quantum systems*. United States: N. p., 2014.
Web. doi:10.1063/1.4879240.

```
Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr, Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr, & Merkli, Marco, E-mail: merkli@mun.ca.
```*Repeated interactions in open quantum systems*. United States. doi:10.1063/1.4879240.

```
Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr, Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr, and Merkli, Marco, E-mail: merkli@mun.ca. Tue .
"Repeated interactions in open quantum systems". United States.
doi:10.1063/1.4879240.
```

```
@article{osti_22306192,
```

title = {Repeated interactions in open quantum systems},

author = {Bruneau, Laurent, E-mail: laurent.bruneau@u-cergy.fr and Joye, Alain, E-mail: Alain.Joye@ujf-grenoble.fr and Merkli, Marco, E-mail: merkli@mun.ca},

abstractNote = {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.},

doi = {10.1063/1.4879240},

journal = {Journal of Mathematical Physics},

number = 7,

volume = 55,

place = {United States},

year = {Tue Jul 15 00:00:00 EDT 2014},

month = {Tue Jul 15 00:00:00 EDT 2014}

}