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arXiv:0905.2558 · Annales Henri Poincaré

Repeated and Continuous Interactions in Open Quantum Systems

Laurent Bruneau, Alain Joye, Marco Merkli

Published Dec 15, 2009• 17 citations
arXivHTMLPDF
DOI
10.1007/s00023-009-0017-8

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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.

arXiv:1305.2472•Journal of Mathematical Physics•Jun 19, 2014•77 citations
We introduce a framework to model the evolution of a class of open quantum systems whose environments periodically undergo an instantaneous non-unitary evolution stage. For the special case of quadratic models, we show how this approach can generalise the formalism of repeated interactions to allow for the preservation of system-environment correlations. Furthermore, its continuous zero-period limit provides a natural description of the evolution of small systems coupled to large environments in negligibly perturbed steady states. We explore the advantages and limitations of this approach in illustrative applications to thermalisation in a simple hopping ring and to the problem of initialising a qubit chain via environmental engineering.
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.