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Ultradiscrete solitons and solvable lattice models

Research Project

Project/Area Number 19540393
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionThe University of Tokyo

Principal Investigator

KUNIBA Atsuo  The University of Tokyo, 大学院・総合文化研究科, 准教授 (70211886)

Co-Investigator(Kenkyū-buntansha) 尾角 正人  大阪大学, 大学院・基礎工学研究科, 准教授 (70221843)
山田 泰彦  神戸大学, 理学部, 教授 (00202383)
Co-Investigator(Renkei-kenkyūsha) OKADO Masato  大阪大学, 大学院・基礎工学研究科, 准教授 (70221843)
山田 泰彦  神戸大学, 理学部, 教授 (00202383)
Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords可積分系 / ソリトン / ベーテ仮説 / 量子群 / ヤン・バクスター方程式 / 箱玉系 / 周期性予想 / クラスター代数 / 非対称排他過程
Research Abstract

超離散ソリトン系の代表的なモデルである箱玉系について, 以下の結果を得た. 多状態かつ箱の容量が任意に非一様な無限系, 2状態で箱の容量が任意で一様な周期系のそれぞれについて, 初期値問題の解のアルゴリズムおよび明示式を得た, 特に明示式として, ソリトン理論や代数曲線の理論に登場するタウ関数やリーマンテータ関数の超離散類似を初めて導出した. この他, T-systemの周期性や多状態非対称排他過程のスペクトルについても結果を得た.

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • Research Products

    (29 results)

All 2009 2008 2007 Other

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (14 results) Book (1 results) Remarks (2 results)

  • [Journal Article] Combinatorial Bethe ansatz andgeneralized periodic box-ball system2008

    • Author(s)
      A. Kuniba and R. Sakamoto
    • Journal Title

      Reviews. Math. Phys 20

      Pages: 493-527

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial Bethe ansatz and generalized periodic box-ball2008

    • Author(s)
      A. Kuniba, R. Sakamoto
    • Journal Title

      Reviews in Mathematical Physics 20

      Pages: 493-527

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of Kirillov-Reshetikhin crystals for nonexceptional types.2008

    • Author(s)
      M. Okado and A. Schilling
    • Journal Title

      Represent. Theory 12

      Pages: 186-207

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Affine geometric crystals and limit of perfect crystals.2008

    • Author(s)
      M. Kashiwara, T. Nakashima and M. Okado
    • Journal Title

      Trans. Amer. Math. Soc. 360

      Pages: 3645-3686

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial Bethe ansatz andultradiscrete Riemann thetafunction with rational characteristics2007

    • Author(s)
      A. Kuniba and R. Sakamoto
    • Journal Title

      Lett. Math. Phys 80

      Pages: 199-209

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tau functions in combinatorial Betheansatz2007

    • Author(s)
      A. Kuniba, R. Sakamoto and Y. Yamada
    • Journal Title

      Nucl. Phys B786[PM]

      Pages: 207-266

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics.2007

    • Author(s)
      A. Kuniba and R. Sakamoto
    • Journal Title

      Lett. Math. Phys. 80

      Pages: 199-209

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tau functions in combinatorial Bethe ansatz.2007

    • Author(s)
      A. Kuniba, R. Sakamoto and Y. Yama
    • Journal Title

      Nucl. Phys. B 786[PM]

      Pages: 207-266

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of crystal bases for Kirillov-Reshetikhin modules of type D.2007

    • Author(s)
      M. Okado
    • Journal Title

      Publ. RIMS 43

      Pages: 977-1004

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perfect crystals for U_q (D_4^<(3)>).2007

    • Author(s)
      M. Kashiwara, K. C. Misra, M. Okado and D. Yamada
    • Journal Title

      J. of Alg. 317

      Pages: 392-423

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] X=M conjecture.2007

    • Author(s)
      M. Okado
    • Journal Title

      MSJ Memoirs 17

      Pages: 43-73

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry and holomorphy of Painlev\'e type systems, Algebraic, analytic and geometric aspects of complex differential equations and their deformations.2007

    • Author(s)
      Y. Sasano and Y. Yamada
    • Journal Title

      Painleve hierarchies, RIMS Kokyuroku Bessatsu B2

      Pages: 215-225

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] T-systemの周期性について2009

    • Author(s)
      井上玲, 伊山修, 国場敦夫, 中西知樹, 鈴木淳史
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Periodicities of T-systems and Y-systems2009

    • Author(s)
      国場敦夫
    • Organizer
      Quantum discrete integrable systems
    • Place of Presentation
      ケンブリッジ大学
    • Year and Date
      2009-03-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] Physical combinatorics of tau function and Bethe ansatz2008

    • Author(s)
      国場敦夫
    • Organizer
      Combinatorics and representation theory
    • Place of Presentation
      名古屋大学
    • Year and Date
      2008-09-01
    • Related Report
      2008 Annual Research Report
  • [Presentation] Physical combinatorics of tau function and Bethe ansatz2008

    • Author(s)
      国場敦夫
    • Organizer
      Aspects of quantum integrability
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Tau functions in combinatorial Bethe ansatz.2008

    • Author(s)
      国場敦夫・坂本玲峰・山田泰彦(発表は坂本玲峰)
    • Organizer
      日本数学会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2008-03-30
    • Related Report
      2007 Annual Research Report
  • [Presentation] Ordinary differential equations and W3 conformal field theory2008

    • Author(s)
      V.V. Bazhanov, 国場敦夫, 鈴木淳史
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Ordinary differential equations and W_3 conformal field theory.2008

    • Author(s)
      V.V.Bazhanov, 国場敦夫, 鈴木淳史(発表は国場)
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Pade近似とPainleve方程式の特殊解.2008

    • Author(s)
      山田泰彦
    • Organizer
      日本数学会無限可積分系セッション一般講演
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] 周期境界条件下の多成分ASEPの固有値2008

    • Author(s)
      有田親史, 国場敦夫, 堺和光, 沢辺剛
    • Organizer
      日本物理学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-23
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Existence of Kirillov-Reshetikhin crystals for nonexceptional types I, BIRS.2008

    • Author(s)
      尾角正人
    • Organizer
      Workshop "Quantum affine Lie algebras, extended affine Lie algebras, and applications"
    • Place of Presentation
      Banff International Research Station, Canada
    • Related Report
      2007 Annual Research Report
  • [Presentation] D^<(1)>n型KR加群の結晶基底について.2008

    • Author(s)
      尾角正人
    • Organizer
      日本数学会2007年度年会
    • Place of Presentation
      埼玉大学
    • Related Report
      2007 Annual Research Report
  • [Presentation] 組合せ論的ベーテ仮説2007

    • Author(s)
      国場敦夫
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2008 Final Research Report
  • [Presentation] 組合せ論的べーテ仮説2007

    • Author(s)
      国場敦夫
    • Organizer
      日本数学会 企画特別講演
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Geometric formulation of discrete Painleve equation and its tropical analogue.2007

    • Author(s)
      山田泰彦
    • Organizer
      研究会「トロピカル幾何学と関連分野」
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2007-09-11
    • Related Report
      2007 Annual Research Report
  • [Book] 日本数学会2007

    • Author(s)
      Atsuo Kuniba and Masato Okado
    • Total Pages
      167
    • Publisher
      Combinatorial Aspect of Integrable Systems, MSJ Memoirs
    • Related Report
      2008 Final Research Report
  • [Remarks] (1)国場敦夫, ベーテ仮説とヤング図形, 数理科学(2007)1月号27-32

    • Related Report
      2008 Final Research Report
  • [Remarks] (2)国場敦夫, ラプラス-ルンゲ-レンツベクトル, Gruppen Pestの始祖的例題, 数理科学(2007)7月号50-55

    • Related Report
      2008 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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