Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

2014/07/31 by Marin Bukov, Luca D'Alessio, Luca D’Alessio +1 · 1,285 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Dissipative system #Floquet theory #Hamiltonian (control theory) #Mathematics #Nonlinear system #Observable #Physics #Quantum many-body systems #Quantum mechanics #Quasiperiodic function #Quasiperiodicity #Theoretical physics #Topological Materials and Phenomena #cond-mat.quant-gas #cond-mat.stat-mech

paper · pdf · doi:10.1080/00018732.2015.1055918

published in Advances In Physics 64(2), 139-226 (Taylor & Francis) · 84 pages, 25 figures, 4 appendices

openalex publication_date 2015/03/04 · arxiv created 2015/08/18 · arxiv updated 2015/08/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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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