Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering |
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Authors: | Marin Bukov Luca D'Alessio Anatoli Polkovnikov |
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Affiliation: | 1. Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USAmbukov@bu.edu;3. Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA;4. Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA |
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Abstract: | 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. |
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Keywords: | 05.45.-a Nonlinear dynamics and chaos 67.85.-d Ultracold gases trapped gases 67.85.Hj Bose–Einstein condensates in optical potentials 71.10.-w Theories and modelsof many-electron systems |
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