Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding
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...
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| Format: | Article |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/1/1 |
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| author | Anton Trushechkin |
| author_facet | Anton Trushechkin |
| author_sort | Anton Trushechkin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T15:01:59Z |
| format | Article |
| id | doaj.art-003313150a82466a89a7c3972f322c1a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T15:01:59Z |
| publishDate | 2023-12-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-003313150a82466a89a7c3972f322c1a2024-01-10T15:03:15ZengMDPI AGMathematics2227-73902023-12-01121110.3390/math12010001Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian EmbeddingAnton Trushechkin0Department of Mathematical Physics, Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina 8, Moscow 119991, RussiaWe 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.https://www.mdpi.com/2227-7390/12/1/1open quantum systemsdecoherenceMarkovian dynamicsnon-Markovian dynamics |
| spellingShingle | Anton Trushechkin Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding Mathematics open quantum systems decoherence Markovian dynamics non-Markovian dynamics |
| title | Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding |
| title_full | Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding |
| title_fullStr | Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding |
| title_full_unstemmed | Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding |
| title_short | Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding |
| title_sort | long term behaviour in an exactly solvable model of pure decoherence and the problem of markovian embedding |
| topic | open quantum systems decoherence Markovian dynamics non-Markovian dynamics |
| url | https://www.mdpi.com/2227-7390/12/1/1 |
| work_keys_str_mv | AT antontrushechkin longtermbehaviourinanexactlysolvablemodelofpuredecoherenceandtheproblemofmarkovianembedding |