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  • Letter
  • Open Access

Steady state of periodically driven quantum systems

Milan Šindelka1,2,* and David Gelbwaser-Klimovsky2,†

  • *Contact author: milan.sindelka@gtiit.edu.cn
  • †Contact author: dgelbi@technion.ac.il
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Phys. Rev. Research 8, L012008 – Published 12 January, 2026

DOI: https://doi.org/10.1103/hsxc-4tgz

Abstract

Periodic driving is used to steer physical systems to unique stationary states or nonequilibrium steady states (NESS), producing enhanced properties inaccessible to nondriven systems. For open quantum systems, characterizing the NESS is challenging and existing results are generally limited to specific types of driving and the Born-Markov approximation. Here, we go beyond these limits by studying a generic periodically driven N-level quantum system interacting with a low-density thermal gas. Exploiting the framework of Floquet scattering theory, we establish general Floquet thermalization conditions constraining the nature of the NESS and the transition rates. Moreover, we examine theoretically the structure of the NESS in the high-temperature limit and find out that the NESS complies, rather surprisingly, with a uniform probability distribution (predicted by the Boltzmann law) for any driving. Numerical calculations illustrate our theoretical elaborations for a simple toy model.

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Phys. Rev. Research 8, L012008– Published 12 January, 2026
  • Received 17 August 2025
  • Accepted 21 December 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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