If the dissipative part of a periodic Lindblad master equation connects all subspaces of the system Hilbert space during any finite fraction of the driving period, then all initial states converge to the same limit cycle.
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Limit cycles in periodically driven open quantum systems
If the dissipative part of a periodic Lindblad master equation connects all subspaces of the system Hilbert space during any finite fraction of the driving period, then all initial states converge to the same limit cycle.