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Aspects in the non-equilibrium dynamics of integrable quantum systems: quantum quench and exact solutions of the Kondo problem

Research Project

Project/Area Number 15K05204
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionOchanomizu University

Principal Investigator

Deguchi Tetsuo  お茶の水女子大学, 基幹研究院, 教授 (70227544)

Co-Investigator(Renkei-kenkyūsha) SATO JUN  東京大学, 先端科学技術研究センター, 助教 (10735723)
KUDO KAZUE  お茶の水女子大学, 基幹研究院, 准教授 (30505574)
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords可積分量子系 / 孤立量子系 / 量子ダイナミクス / ベーテ仮設 / ダークソリトン / 非平衡 / 量子多体系 / 可積分系 / ダイナミクス / 緩和 / 量子クエンチ / 1次元ボース気体 / 量子XXX鎖 / 量子ハイゼンベルグ鎖 / 局所磁化 / 時間発展 / 非平衡系
Outline of Final Research Achievements

Recently, relaxation behaviors of isolated quantum systems were observed in cold atomic experiments. It is conjecture that in non-integrable systems expectation values of localized physical quantities approach values associated with the micro-canonical ensemble (thermalization), while in integrable systems values associated with the generalized Gibbs ensemble. In this research we studied aspects of non-equilibrium dynamics for integrable systems. For the one-dimensional Bose gas (the Lieb-Liniger model), some superposition of one-hole states shows a density profile consistent with a classical dark soliton in the weak coupling case. We call it a quantum dark soliton state. In the one-dimensional Heisenberg model we constructed a quantum state that has a localized magnetization profile, and derived its time evolution with the Bethe ansatz. We have observed that it relaxes very slowly almost proportional to some power of time variable.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (19 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (3 results) Journal Article (4 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 4 results,  Open Access: 1 results,  Acknowledgement Compliant: 2 results) Presentation (11 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results) Remarks (1 results)

  • [Int'l Joint Research] Department of Physics/Tamkang University(台湾)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Massachusetts Boston(米国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Department of Physics/University of Massachusetts Boston(米国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Multi-qudit states generated by unitary braid quantum gates based on Temperley-Lieb algebra2017

    • Author(s)
      C.L. Ho, T. Deguchi
    • Journal Title

      Europhysics Letters

      Volume: 118 Issue: 4 Pages: 40001-40001

    • DOI

      10.1209/0295-5075/118/40001

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Quantum states of dark solitons in the 1D Bose gas2016

    • Author(s)
      Jun Sato, Rina Kanamoto, Eriko Kaminishi, and Tetsuo Deguchi
    • Journal Title

      New Journal of Physics

      Volume: 18 Issue: 7 Pages: 075008-075008

    • DOI

      10.1088/1367-2630/18/7/075008

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Exact quantum numbers of collapsed and non-collapsed 2-string solutions in the Heisenberg spin chain2016

    • Author(s)
      T. Deguchi and P. R. Giri,
    • Journal Title

      J. Phys. A: Theor. Math.

      Volume: 印刷中 Issue: 17 Pages: 174001-174001

    • DOI

      10.1088/1751-8113/49/17/174001

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Crossover temperature of the spin-1/2 XXZ chain with an impurity2016

    • Author(s)
      R. Yahagi, J. Sato and T. Deguchi
    • Journal Title

      J. Phys.: Conf. Ser.

      Volume: 印刷中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 量子XXZ鎖に対する厳密なBethe 量子数とBethe 根2018

    • Author(s)
      井元隆史、出口哲生
    • Organizer
      日本物理学会 第73回年次大会、東京理科大学野田キャンパス
    • Related Report
      2017 Annual Research Report
  • [Presentation] 1次元自由フェルミオン系(TG気体)における密度プロファイルの厳密な時間発展2018

    • Author(s)
      金城佳世、出口哲生
    • Organizer
      日本物理学会 第73回年次大会、東京理科大学野田キャンパス
    • Related Report
      2017 Annual Research Report
  • [Presentation] 捻り境界条件下のスピン1/2 XXX鎖の厳密な量子数:下向きスピン2個の場合2018

    • Author(s)
      出口哲生、井元隆史
    • Organizer
      日本物理学会 第73回年次大会、東京理科大学野田キャンパス
    • Related Report
      2017 Annual Research Report
  • [Presentation] Bethe Ansatz equation のsingular solution に対応するスカラー積公式2017

    • Author(s)
      渡邉聡、井元隆史、出口哲生
    • Organizer
      日本物理学会第72回年次大会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2017-03-20
    • Related Report
      2016 Research-status Report
  • [Presentation] XXX鎖のtwo down spin に対する固有ベクトルを用いたBethe Ansatz の完全性について2017

    • Author(s)
      井元隆史、渡邉聡、出口哲生
    • Organizer
      日本物理学会第72回年次大会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2017-03-20
    • Related Report
      2016 Research-status Report
  • [Presentation] 量子XXX鎖と量子XXZ鎖に関する量子数の厳密な対応2017

    • Author(s)
      井元隆史、出口哲生
    • Organizer
      日本物理学会 2017年秋季大会、岩手大学上田キャンパス
    • Related Report
      2017 Annual Research Report
  • [Presentation] 量子XXZ鎖の局所演算子の形状因子公式と量子ダイナミクスへの応用2016

    • Author(s)
      出口哲生
    • Organizer
      日本物理学会2016年秋季大会
    • Place of Presentation
      金沢大学角間キャンパス
    • Year and Date
      2016-09-16
    • Related Report
      2016 Research-status Report
  • [Presentation] 可積分量子スピン系における局在波の非平衡緩和ダイナミクスと孤立量子系の熱化、そして1次元ボース気体との比較2016

    • Author(s)
      出口哲生
    • Organizer
      日本物理学会2016年秋季大会
    • Place of Presentation
      金沢大学角間キャンパス
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
  • [Presentation] 任意サイズ量子XXZ鎖の下向きスピン2個の固有状態の完全性2015

    • Author(s)
      出口哲生, Pulak Ranjan Giri
    • Organizer
      日本物理学会  2015年秋季大会
    • Place of Presentation
      関西大学千里山キャンパス
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] Exact non-equilibrium dynamics in 1D integrable quantum systems2015

    • Author(s)
      T. Deguchi
    • Organizer
      "Thermalization in isolated quantum systems'', New Frontiers in Non-equilibrium Physics 2015
    • Place of Presentation
      Yukawa Institute for Theoretical Physics, Kyoto University
    • Year and Date
      2015-08-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Exact non-equilibrium dynamics in 1D integrable quantum many-body models2015

    • Author(s)
      T. Deguchi
    • Organizer
      Beyond Integrability. The Mathematics and Physics of Integrability and Its Breaking in Low-dimensional Strongly Correlated Qunantum Phenomena
    • Place of Presentation
      CRM, Montreal, Canada
    • Year and Date
      2015-07-13
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] Deguchi Laboratory

    • URL

      http://www.phys.ocha.ac.jp/deguchilab/home.html

    • Related Report
      2016 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2022-08-18  

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