Floquet resonant states and validity of the Floquet-Magnus expansion in the periodically driven Friedrichs models

Abstract

The Floquet eigenvalue problem is analyzed for periodically driven Friedrichs models on discrete and continuous space. In the high-frequency regime, there exists a Floquet bound state consistent with the Floquet-Magnus expansion in the discrete Friedrichs model, while it is not the case in the continuous model. In the latter case, however, the bound state predicted by the Floquet-Magnus expansion appears as a metastable state whose lifetime diverges in the limit of large frequencies. We obtain the lifetime by evaluating the imaginary part of the quasi-energy of the Floquet resonant state. In the low-frequency regime, there is no Floquet bound state and instead the Floquet resonant state with exponentially small imaginary part of the quasi-energy appears, which is understood as the quantum tunneling in the energy space.

arXiv comment5 pages, 3 figures

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• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Towards large-Chern-number topological phases by periodic quenching
• Effective Floquet-Gibbs states for dissipative quantum systems
• Floquet prethermalization in periodically driven classical spin systems
• Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system
• Brillouin-Wigner Theory for Floquet Topological Phase Transitions in Spin-orbit Coupled Materials
• Floquet bound states around defects and adatoms in graphene
• Dynamics of fluctuation correlation in periodically driven classical system
• Long time asymptotic state of periodically driven open quantum systems
• Resonances in a periodically driven bosonic system
• Divergence of the Floquet-Magnus expansion in a periodically driven one-body system with energy localization
• Periodically-driven Kondo impurity in nonequilibrium steady states
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Statistical prethermalization in randomly kicked many-body classical rotor system