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New trends in integrable systems, non-equilibrium, duality and quantum geometry

Research Project

Project/Area Number 18H01141
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionThe University of Tokyo

Principal Investigator

Kuniba Atsuo  東京大学, 大学院総合文化研究科, 教授 (70211886)

Co-Investigator(Kenkyū-buntansha) 鈴木 淳史  静岡大学, 理学部, 教授 (40222062)
松尾 泰  東京大学, 大学院理学系研究科(理学部), 教授 (50202320)
笹本 智弘  東京工業大学, 理学院, 教授 (70332640)
Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥10,140,000 (Direct Cost: ¥7,800,000、Indirect Cost: ¥2,340,000)
Fiscal Year 2020: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2019: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2018: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords量子群 / 共形場理論 / 双対性 / 排他過程 / 可積分確率 / 動的相関関数 / 一般化流体力学 / 一般可流体力学 / 可積分系 / 超対称ゲージ理論 / 非平衡動力学 / スピン鎖 / ベーテ仮説 / 確率過程 / 量子スピン鎖 / 非平衡 / 量子幾何
Outline of Final Research Achievements

By means of the common key structure of integrability, many outstanding problems in mathematical physics are studied, which has led to fruitful results. Kuniba has constructed K matrices and quantum spin chains associated with Onsager algebra systematically and described the randomized box-ball system in terms of generalized hydrodynamics. Matsuo clarified the duality in quantum toroidal algebra, constructed a minimal model in Web of W algebras and q-deformed corner VOA and obtained applications to matrix models. Suzuki obtained dynamical 2 point correlation function for general XX spin model and accurate evaluation of the dynamical structure factors partly also in the XXZ spin model. Sasamoto obtained exact results including fluctuations of positions of particles in a 2 species asymmetric exclusion process and the large deviation principle in a symmetric exclusion process

Academic Significance and Societal Importance of the Research Achievements

可積分系は数学的に厳密な解析が実行可能な系であり,その研究は豊かな歴史と蓄積がある.現代においても数学と理論物理学の最先端の知見が結集する分野として数理科学の中で傑出した位置を占め,その成果は数学と物理の双方に波及しながら発展している.
本研究は特に近年可積分性が威力を発揮している分野の専門家4名によるものであり,一般化流体力学,
ゲージ理論,超弦理論の代数的基礎,量子スピン系の動的相関関数,排他確率過程の諸種の揺らぎ等について極めて技術的に高く精密な結果が数多く得られた.関連する話題は広く,特に2年目に開催した国際ワークショップには多くの研究者が来訪し,有意義な研究交流の機会となった.

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (51 results)

All 2021 2020 2019 Other

All Int'l Joint Research (11 results) Journal Article (17 results) (of which Int'l Joint Research: 12 results,  Peer Reviewed: 17 results,  Open Access: 11 results) Presentation (20 results) (of which Int'l Joint Research: 13 results,  Invited: 18 results) Remarks (1 results) Funded Workshop (2 results)

  • [Int'l Joint Research] CEA/Saclay 理論物理学研究所(フランス)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] 国立台湾大学(その他の国・地域)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] KIAS(韓国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] メルボルン大学(オーストラリア)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] ブッパタール大学(ドイツ)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Saclay理論物理研究所/モデル化理論物理研究所/Lyon大学(フランス)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Wuppertal 大学(ドイツ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Manitoba大学(カナダ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Saclay理論物理研究所/モデル理論物理研究所/Lyon大学(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Wuppertal大学(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Manitoba大学(カナダ)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] A remark on renormalization group theoretical perturbation in a class of ordinary differential equations2021

    • Author(s)
      Atsuo Kuniba
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: 2021 Issue: 1

    • DOI

      10.1093/ptep/ptaa178

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime2021

    • Author(s)
      C. Babenko, F. Gohmann, K. Kozlowski, J. Suzuki
    • Journal Title

      J. Math. Phys.

      Volume: 62 Issue: 4

    • DOI

      10.1063/5.0039863

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition2021

    • Author(s)
      Takashi Imamura, Kirone Mallick, Tomohiro Sasamoto
    • Journal Title

      Commun. Math. Phys.

      Volume: 出版予定のため未定

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Determinantal structures in the q-Whittaker measure2021

    • Author(s)
      Takashi Imamura, Matteo Mucciconi, Tomohiro Sasamoto
    • Journal Title

      Adv. Pure Appl. Math.

      Volume: 出版予定のため未定

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Exact real-time longitudinal correlation functions of the massive XXZ chain2021

    • Author(s)
      C. Babenko, F. Goehmann, K. K. Kozlowski, J. Sirker, J. Suzuki
    • Journal Title

      Physical Review Letters

      Volume: 出版予定のため未定

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Generalized hydrodynamics in complete box-ball system for U_q(sl_n)2021

    • Author(s)
      A. Kuniba,G. Misguich and V. Pasquier
    • Journal Title

      SciPost

      Volume: 出版予定のため未定

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Dimensional oxidization on coset space2020

    • Author(s)
      K. Harada, P. -M. Ho, Y. Matsuo, A. Watanabe
    • Journal Title

      JHEP

      Volume: 10 Issue: 10 Pages: 198-198

    • DOI

      10.1007/jhep10(2020)198

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Generalized hydrodynamics in box-ball system2020

    • Author(s)
      Atsuo Kuniba, Gregoire Misguich, Vincent Pasquier
    • Journal Title

      J. Phys. A: Math. Theor

      Volume: 53 Issue: 40 Pages: 404001-404001

    • DOI

      10.1088/1751-8121/abadb9

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain2020

    • Author(s)
      Frank Goehmann, Karol K. Kozlowski, Junji Suzuki
    • Journal Title

      Journal of Mathematical Physics

      Volume: 61 Issue: 1

    • DOI

      10.1063/1.5111039

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Long-time large-distance asymptotics of the transverse correlation functions of the XX chain in the spacelike regime2020

    • Author(s)
      Frank Goehmann, Karol K. Kozlowski, Junji Suzuki
    • Journal Title

      Letters in Mathematical Physics

      Volume: 2020 Issue: 7 Pages: 1783-1797

    • DOI

      10.1007/s11005-020-01276-y

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Thermodynamics of the spin-1/2 Heisenberg-Ising chain at high temperatures: a rigorous approach2020

    • Author(s)
      F. Goehmann, S. Goomannee, K. K. Kozlowski, J. Suzuki
    • Journal Title

      Communications in Mathematical Physics

      Volume: ー Issue: 1 Pages: 623-673

    • DOI

      10.1007/s00220-020-03749-6

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A note on S-dual basis in free fermion system2020

    • Author(s)
      S. Sasa, A. Watanabe, Y. Matsuo
    • Journal Title

      PTEP

      Volume: 2020 Issue: 2

    • DOI

      10.1093/ptep/ptz158

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quantum spin chains from Onsager algebras and reflection K-matrices2019

    • Author(s)
      A. Kuniba, V. Pasquier
    • Journal Title

      Nuclear Physics B

      Volume: 949 Pages: 114792-114792

    • DOI

      10.1016/j.nuclphysb.2019.114792

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Equilibrium dynamics of the XX chain2019

    • Author(s)
      Frank Goehmann, Karol K. Kozlowski, Jesko Sirker, Junji Suzuki
    • Journal Title

      Physical Review B

      Volume: 100 Issue: 15 Pages: 155428-155428

    • DOI

      10.1103/physrevb.100.155428

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition2019

    • Author(s)
      Hiroki Moriya, Rikuo Nagao, Tomohiro Sasamoto,
    • Journal Title

      J. Stat. Mech.

      Volume: 2019 Issue: 6 Pages: 063105-063105

    • DOI

      10.1088/1742-5468/ab1dd6

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A^{(1)}_{n-1}$2019

    • Author(s)
      Atsuo Kuniba and Masato Okado
    • Journal Title

      Journal of Integrable Systems

      Volume: 4 Issue: 1 Pages: 1-10

    • DOI

      10.1093/integr/xyz013

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Reflection $K$ matrices associated with an Onsager coideal of $U_p(A^{(1)}_{n-1}), U_p(B^{(1)}_n), U_p(D^{(1)}_n)$ and $U_p(D^{(2)}_{n+1})$2019

    • Author(s)
      Atsuo Kuniba, Masato Okado and Akihito Yoneyama
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 52 Issue: 37 Pages: 375202-375202

    • DOI

      10.1088/1751-8121/ab3715

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] q-Deformation of Corner Vertex Operator Algebras by Miura Transformation2021

    • Author(s)
      松尾 泰
    • Organizer
      Randomness, Integrability and Representation Theory in Quantum Field Theory 2021
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Nambu-bracket and M-theory2020

    • Author(s)
      松尾 泰
    • Organizer
      Space-time topology behind formation of micro-macro magneto-vortical structure manifested by Nambu mechanics
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Generalized hydrodynamics for randomized box-ball system2020

    • Author(s)
      国場 敦夫
    • Organizer
      The Asia-Pacific Integrable Online Seminars
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spin current statistics for the quantum 1D XX spin chain and the Bessel kernel2020

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      CMI-HIMR Integrable Probability Summer School
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Current moment formulas for 1D exclusion processes2020

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      New Connections in Integrable Systems
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Generalized hydrodynamics in box-ball systems2020

    • Author(s)
      A. Kuniba
    • Organizer
      Baxter 2020: Frontiers in Integrability
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the random matrix type multiple contour integrals for particle systems2020

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      Spectra of Random Operators and Related Topics
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Invited
  • [Presentation] Real topological vertex, boundary state, and quantum toroidal algebra2020

    • Author(s)
      Yutaka Matsuo
    • Organizer
      Rikkyo Math-Phys 2020
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
  • [Presentation] Fredholm determinants and the equilibrium dynamics of quantum spin chains "Correlations in Integrable Quantum Many-Body Systems IV"2019

    • Author(s)
      J. Suzuki
    • Organizer
      Correlations in Integrable Quantum Many-Body Systems IV
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Randomized box-ball systems, limit shape of soliton distributions and thermodynamic Bethe ansatz2019

    • Author(s)
      A. Kuniba
    • Organizer
      Workshop on Recent Progress in Mathematical and Statistical Physics
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Analytic confirmation of a nonlinear fluctuating hydrodynamics prediction for a two species asymmetric exclusion process2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      Emergent Hydrodynamics In Low Dimensional Quantum Systems
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Exact confirmation of the nonlinear fluctuating hydrodynamics for a two species asymmetric exclusion process2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      STATPHYS27
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Large deviation of spin current for the 1D XX spin chain with domain wall boundary condition2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      Classical and Quantum Integrable Systems 2019
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spin current for the quantum 1D XX spin chain and the Bessel kernel2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      Interactions between commutative and non-commutative probability
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Invited
  • [Presentation] Spin current for the quantum 1D XX spin chain and the Bessel kernel2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      School and Workshop on Random Matrix Theory and Point Processes
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Large deviation of spin current for the 1D XX spin chain with domain wall boundary condition2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      Workshop on Recent Progress in Mathematical and Statistical Physics
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Invited
  • [Presentation] Exact current fluctuations for 1D non-equilibrium many-body systems2019

    • Author(s)
      Tomohiro Sasamoto
    • Organizer
      TokyoTech and IIT Guwahati Joint Workshop: Condensed Matter and High-Energy Physics
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Invited
  • [Presentation] Fluctuations for a two species asymmetric exclusion process2019

    • Author(s)
      笹本 智弘
    • Organizer
      18th Stochastic Analysis on Large Scale Interacting Systems
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Invited
  • [Presentation] Large deviations for 1D exclusion process2019

    • Author(s)
      笹本 智弘
    • Organizer
      Stochastic Analysis on Particle Systems
    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Invited
  • [Presentation] Fredholm determinants and the equilibrium dynamics of quantum spin chains2019

    • Author(s)
      J. Suzuki
    • Organizer
      Correlations in Integrable Quantum Many-Body Systems IV
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] Workshop new trends in integrable systems 2019

    • URL

      https://indico2.riken.jp/event/3020/

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
  • [Funded Workshop] Workshop new trends in integrable systems 20192019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] Workshop new trends in integrable systems 20192019

    • Related Report
      2018 Annual Research Report

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Published: 2018-04-23   Modified: 2022-01-27  

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