Effective Floquet-Gibbs states for dissipative quantum systems

Tatsuhiko Shirai, Juzar Thingna, Takashi Mori, Sergey Denisov, Peter Hänggi, Seiji Miyashita

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using the so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.

Original languageEnglish
Article number053008
JournalNew Journal of Physics
Issue number5
Publication statusPublished - 2016 May 1
Externally publishedYes


  • Non-equilibrium asymptotic states
  • Open quantum system
  • Time-periodic driving field

ASJC Scopus subject areas

  • General Physics and Astronomy


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