### Abstract

We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak-coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.

Original language | English |
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Article number | 030101 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 91 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 Mar 3 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*91*(3), [030101]. https://doi.org/10.1103/PhysRevE.91.030101

**Condition for emergence of the Floquet-Gibbs state in periodically driven open systems.** / Shirai, Tatsuhiko; Mori, Takashi; Miyashita, Seiji.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 91, no. 3, 030101. https://doi.org/10.1103/PhysRevE.91.030101

}

TY - JOUR

T1 - Condition for emergence of the Floquet-Gibbs state in periodically driven open systems

AU - Shirai, Tatsuhiko

AU - Mori, Takashi

AU - Miyashita, Seiji

PY - 2015/3/3

Y1 - 2015/3/3

N2 - We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak-coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.

AB - We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak-coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.

UR - http://www.scopus.com/inward/record.url?scp=84924778587&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924778587&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.91.030101

DO - 10.1103/PhysRevE.91.030101

M3 - Article

VL - 91

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

M1 - 030101

ER -