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.

5 pages, 3 figures

References in corpus (6)

• Photovoltaic Hall effect in graphene
• The Magnus expansion and some of its applications
• Driven quantum transport on the nanoscale
• Equilibrium states of generic quantum systems subject to periodic driving
• Periodically driven ergodic and many-body localized quantum systems
• Parametric instability in periodically driven Luttinger liquids

Cited by in corpus (7)

• Brillouin-Wigner Theory for Floquet Topological Phase Transitions in Spin-orbit Coupled Materials
• 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
• 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