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Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding

Author

Listed:
  • Anton Trushechkin

    (Department of Mathematical Physics, Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina 8, Moscow 119991, Russia
    Institute for Theoretical Physics III, Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
    Department of Mathematics, National University of Science and Technology MISIS, Leninskiy Prospekt 4, Moscow 119049, Russia)

Abstract

We consider a well-known, exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental question of the quantum–classical transition. It is worth studying how the long-term rate of decoherence depends on the spectral density characterising the system–bath interaction in this exactly solvable model. Secondly, we address a more general problem of the Markovian embedding of non-Markovian open system dynamics. It is often assumed that a non-Markovian open quantum system can be embedded into a larger Markovian system. However, we show that such embedding is possible only for Ohmic spectral densities (for the case of a positive bath temperature) and is impossible for both sub- and super-Ohmic spectral densities. On the other hand, for Ohmic spectral densities, an asymptotic large-time Markovianity (in terms of the quantum regression formula) takes place.

Suggested Citation

  • Anton Trushechkin, 2023. "Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding," Mathematics, MDPI, vol. 12(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:1-:d:1302799
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