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Letters in Mathematical Physics

, Volume 107, Issue 7, pp 1215–1233 | Cite as

Completely positive dynamical semigroups and quantum resonance theory

  • Martin KönenbergEmail author
  • Marco Merkli
Article

Abstract

Starting from a microscopic system–environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the following two properties: It is (linearly) small in the system–environment coupling constant for all times, and it vanishes exponentially quickly in the large time limit. Our approach is based on the quantum dynamical resonance theory.

Keywords

Open quantum system Quantum resonances Dynamical semigroup Complete positivity 

Mathematics Subject Classification

82C10 81S22 

Notes

Acknowledgements

This work has been supported by an NSERC Discovery Grant and an NSERC Discovery Grant Accelerator. We thank an anonymous referee for useful comments and for inciting us to explain the derivation of (2.11), resulting in Sect. 2.1.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial UniversitySt. John’sCanada
  2. 2.Fachbereich MathematikUniversität StuttgartStuttgartGermany

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