skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

Abstract

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on themore » prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.« less

Authors:
 [1];  [1];  [2]
  1. Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)
  2. Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 (Japan)
Publication Date:
OSTI Identifier:
22560308
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 367; Journal Issue: Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; ENERGY ABSORPTION; HAMILTONIANS; MANY-BODY PROBLEM; PERIODICITY; QUANTUM SYSTEMS; SERIES EXPANSION; THERMALIZATION; THERMODYNAMICS; TRANSIENTS

Citation Formats

Kuwahara, Tomotaka, WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Mori, Takashi, and Saito, Keiji. Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.01.012.
Kuwahara, Tomotaka, WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Mori, Takashi, & Saito, Keiji. Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. United States. https://doi.org/10.1016/J.AOP.2016.01.012
Kuwahara, Tomotaka, WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Mori, Takashi, and Saito, Keiji. 2016. "Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems". United States. https://doi.org/10.1016/J.AOP.2016.01.012.
@article{osti_22560308,
title = {Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems},
author = {Kuwahara, Tomotaka and WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577 and Mori, Takashi and Saito, Keiji},
abstractNote = {This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.},
doi = {10.1016/J.AOP.2016.01.012},
url = {https://www.osti.gov/biblio/22560308}, journal = {Annals of Physics},
issn = {0003-4916},
number = Complete,
volume = 367,
place = {United States},
year = {2016},
month = {4}
}