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  • Open Access

Effective Floquet Lindblad generators from spectral unwinding

Görkem D. Dinc, André Eckardt, and Alexander Schnell*

  • *Contact author: schnell@tu-berlin.de
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Phys. Rev. A 111, 062216 – Published 25 June, 2025

DOI: https://doi.org/10.1103/x2qh-12gg

Abstract

A mathematical description of the reduced dynamics of an open quantum system can often be given in terms of a completely positive and trace-preserving map, also known as a quantum channel. In a seminal work by Wolf et al. [Phys. Rev. Lett. 101, 150402 (2008)], it was shown that deciding whether a given quantum channel was generated from an underlying effective Markovian dynamics, with time-independent generator of Lindblad form, is generally an NP-hard problem. The difficulty is related to the fact that one has to search through all possible branches of the operator logarithm of the map in order to identify if any of the resulting effective generators is of Lindblad form. In this work we show that in cases where one has access to the full reduced dynamics at all previous times (the dynamical map) one can significantly facilitate the search for an effective generator by making use of Floquet theory. By performing a spectral unwinding such that the effective micromotion is minimized, the effective Floquet generator is often an excellent candidate for an effective generator of Lindblad form. This significantly reduces the complexity of the search for an effective Lindbladian in many (though not all) cases. Our results are relevant for engineering Floquet Lindbladians in complex many-body systems.

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Phys. Rev. A 111, 062216– Published 25 June, 2025
  • Received 17 December 2024
  • Revised 22 February 2025
  • Accepted 2 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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