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Annales Henri Poincaré

, Volume 16, Issue 6, pp 1397–1427 | Cite as

Overlapping Resonances in Open Quantum Systems

  • Marco MerkliEmail author
  • Haifeng Song
Article

Abstract

An N-level quantum system is coupled to a bosonic heat reservoir at positive temperature. We analyze the system–reservoir dynamics in the following regime: the strength λ of the system–reservoir coupling is fixed and small, but larger than the spacing σ of system energy levels. For vanishing σ there is a manifold of invariant system–reservoir states and for σ > 0 the only invariant state is the joint equilibrium. The manifold is invariant for σ = 0 but becomes quasi-invariant for σ > 0. Namely, on a first time-scale of the order 1/λ2, initial states approach the manifold. Then, they converge to the joint equilibrium state on a much larger time-scale of the order λ2/σ 2. We give a detailed expansion of the system–reservoir evolution showing the above scenario.

Keywords

Density Matrix Reduce Density Matrix Simple Eigenvalue Open Quantum System Density Matrix Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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