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

Anton Trushechkin ()
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Anton Trushechkin: Department of Mathematical Physics, Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina 8, Moscow 119991, Russia

Mathematics, 2023, vol. 12, issue 1, 1-18

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.

Keywords: open quantum systems; decoherence; Markovian dynamics; non-Markovian dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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