Asymptotic relaxation in quantum Markovian dynamics
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914215643578368 |
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| author | Di Meglio, Giovanni Chruściński, Dariusz Audenaert, Koenraad Plenio, Martin B. Huelga, Susana F. |
| author_facet | Di Meglio, Giovanni Chruściński, Dariusz Audenaert, Koenraad Plenio, Martin B. Huelga, Susana F. |
| contents | We investigate the long-time behavior of quantum Markovian dynamics generated by time-dependent Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equations. We introduce a notion of weak relaxation and derive sufficient conditions guaranteeing asymptotic independence from the initial state. Our results provide a quantitative extension of the Spohn-Frigerio theorem to time-dependent generators, yielding explicit contraction bounds in terms of the instantaneous steady state and time-integrated dissipation rates. For a class of microscopically derived master equations, we further obtain a graph-theoretic characterization of the aforementioned conditions that directly links the structure of the jump operators to the relaxation properties. The general theory is illustrated by applications to driven finite-level systems, including a detailed three-level example, and is extended to a non-Markovian setting by means of time-local master equations that become of GKLS form at long times. These findings pave the way for the development of a more general theory of relaxation beyond the Markovian case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic relaxation in quantum Markovian dynamics Di Meglio, Giovanni Chruściński, Dariusz Audenaert, Koenraad Plenio, Martin B. Huelga, Susana F. Quantum Physics We investigate the long-time behavior of quantum Markovian dynamics generated by time-dependent Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equations. We introduce a notion of weak relaxation and derive sufficient conditions guaranteeing asymptotic independence from the initial state. Our results provide a quantitative extension of the Spohn-Frigerio theorem to time-dependent generators, yielding explicit contraction bounds in terms of the instantaneous steady state and time-integrated dissipation rates. For a class of microscopically derived master equations, we further obtain a graph-theoretic characterization of the aforementioned conditions that directly links the structure of the jump operators to the relaxation properties. The general theory is illustrated by applications to driven finite-level systems, including a detailed three-level example, and is extended to a non-Markovian setting by means of time-local master equations that become of GKLS form at long times. These findings pave the way for the development of a more general theory of relaxation beyond the Markovian case. |
| title | Asymptotic relaxation in quantum Markovian dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.14313 |