# Periodic steady regime and interference in a periodically driven quantum system.

TL;DR: The case of a quantum Ising chain periodically driven across the critical point is discussed, finding that, as a result of quantum coherence, the system never reaches an infinite temperature state.

Abstract: We study the coherent dynamics of a quantum many-body system subject to a time-periodic driving. We argue that in many cases, destructive interference in time makes most of the quantum averages time periodic, after an initial transient. We discuss in detail the case of a quantum Ising chain periodically driven across the critical point, finding that, as a result of quantum coherence, the system never reaches an infinite temperature state. Floquet resonance effects are moreover observed in the frequency dependence of the various observables, which display a sequence of well-defined peaks or dips. Extensions to nonintegrable systems are discussed.

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TL;DR: In this article, a general overview of the high-frequency regime in periodically driven systems and three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian are identified.

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 particul...

942 citations

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TL;DR: In this article, a general framework to understand the long but finite time behavior of many-body quantum systems under periodic driving is provided, where the authors focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system.

316 citations

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TL;DR: In this article, the authors studied the dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time, and established conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space.

300 citations

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TL;DR: In this article, a theory of periodically driven, many-body localized (MBL) systems is presented, where the Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL.

200 citations

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TL;DR: In this article, a review of theoretical approaches to thermal equilibrium in isolated quantum systems is presented, including thermalization and prethermalization, where there is a clear separation in relevant time scales and has several different physical origins depending on individual systems.

Abstract: The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal system to study the nonequilibrium dynamics in isolated quantum systems, triggering intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation in relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

200 citations