### 抄録

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.

元の言語 | English |
---|---|

ページ（範囲） | 96-124 |

ページ数 | 29 |

ジャーナル | Annals of Physics |

巻 | 367 |

DOI | |

出版物ステータス | Published - 2016 4 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### これを引用

*Annals of Physics*,

*367*, 96-124. https://doi.org/10.1016/j.aop.2016.01.012

**Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems.** / Kuwahara, Tomotaka; Mori, Takashi; Saitou, Keiji.

研究成果: Article

*Annals of Physics*, 巻. 367, pp. 96-124. https://doi.org/10.1016/j.aop.2016.01.012

}

TY - JOUR

T1 - Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

AU - Kuwahara, Tomotaka

AU - Mori, Takashi

AU - Saitou, Keiji

PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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.

AB - 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.

KW - Energy absorption

KW - Floquet-Magnus expansion

KW - Generic few-body Hamiltonian

KW - Periodically driven system

KW - Prethermalization

KW - Transient dynamics

UR - http://www.scopus.com/inward/record.url?scp=84958045504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958045504&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2016.01.012

DO - 10.1016/j.aop.2016.01.012

M3 - Article

AN - SCOPUS:84958045504

VL - 367

SP - 96

EP - 124

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -