Floquet–Gibbs state in open quantum systems

Tatsuhiko Shirai*, Takashi Mori, Seiji Miyashita

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We study long-time asymptotic states of periodically driven quantum systems coupled to a thermal bath. In order to describe a class of such a system, we introduce the Floquet–Gibbs state, i.e. the state whose density matrix is diagonalized in the basis of the Floquet state of the system Hamiltonian, and its diagonal element obeys the Boltzmann distribution over its Floquet quasienergy. We obtain sufficient conditions for the realization of the Floquet–Gibbs state in a system with infinitesimal system-bath coupling [T. Shirai et al., Phys. Rev. E 91, 030101 (2015)]. These conditions severely restrict a class of suitable physical models attaining the Floquet–Gibbs state. We also show that some of the conditions can be lifted by imposing conditions on timescales of the thermal bath with the aid of the truncated Floquet Hamiltonian in the Floquet–Magnus expansion [T. Shirai et al., New J. Phys. 18, 053008 (2016)]. In this paper, we give an overview of this theory and reconsider it by looking at the dynamics from a rotating frame.

Original languageEnglish
Pages (from-to)323-333
Number of pages11
JournalEuropean Physical Journal: Special Topics
Issue number3-4
Publication statusPublished - 2018 Sept 1
Externally publishedYes

ASJC Scopus subject areas

  • Materials Science(all)
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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