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arXiv · 2410.14313

Asymptotic relaxation in quantum Markovian dynamics

Giovanni Di Meglio·Dariusz Chruściński·Koenraad Audenaert·Martin B. Plenio·Susana F. Huelga
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Abstract

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.

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Giovanni Di Meglio, Dariusz Chruściński, Koenraad Audenaert, Martin B. Plenio, Susana F. Huelga. 2025-12-22. Asymptotic relaxation in quantum Markovian dynamics. https://doi.org/10.1063/5.0321469

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