Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
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Citation (published version)Marin Bukov, Luca D'Alessio, Anatoli Polkovnikov. 2015. "Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering." ADVANCES IN PHYSICS, Volume 64, Issue 2, pp. 139 - 226 (88). https://doi.org/10.1080/00018732.2015.1055918
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.