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

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.

6pages, 3 figures

References in corpus (9)

• The Magnus expansion and some of its applications
• Two-level systems driven by large-amplitude fields
• Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
• Dissipative Floquet Topological Systems
• Tuning the Mott transition in a Bose-Einstein condensate by multi-photon absorption
• Materials design from non-equilibrium steady states: driven graphene as a tunable semiconductor with topological properties
• Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation
• Coherent control of interacting particles using dynamical and Aharonov-Bohm phases
• A perturbative method for nonequilibrium steady state of open quantum systems

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