### 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 |

### ASJC Scopus subject areas

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

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## Cite this

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

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