Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems

2015/09/30 by Takashi Mori, Tomotaka Kuwahara, Keiji Saito · 5 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Exponential growth #Floquet theory #Hamiltonian (control theory) #Integrable system #Mathematical physics #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum system #Relaxation (psychology) #Statistical physics #cond-mat.quant-gas #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1103/physrevlett.116.120401

published as Phys. Rev. Lett. 116, 120401 (2016) · 5+6 pages, 3 figures; typos corrected

openalex publication_date 2016/03/21 · arxiv created 2017/03/17 · arxiv updated 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion is a quasiconserved quantity in a long time scale. These two general properties lead to an intriguing classification on the initial stage of relaxation, one of which is similar to the prethermalization phenomenon in nearly integrable systems.

Citations

• Fate of Many-Body Localization Under Periodic Driving
• Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
• Many-body physics with ultracold gases
• Exact Relaxation Dynamics of a Localized Many-Body State in the 1D Bose Gas
• The Magnus expansion and some of its applications
• Floquet resonant states and validity of the Floquet-Magnus expansion in the periodically driven Friedrichs models
• Chaos and Quantum Thermalization
• Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices
• Interaction Quench in the Hubbard Model
• Quantum statistical mechanics in a closed system
• Freezing a quantum magnet by repeated quantum interference: An experimental realization
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

Cited by

• Tunable Floquet selection rules in a driven Ising chain
• Emergent Hydrodynamics in Nonequilibrium Quantum Systems
• Dissipative Floquet Majorana Modes in Proximity-Induced Topological Superconductors
• Adiabatic perturbation theory and geometry of periodically-driven systems
• Spin-dependent Andreev reflection in spin-orbit coupled systems by breaking time-reversal symmetry