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Algebraic Study of Compleetely Integrable Systems

Research Project

Project/Area Number 08640512
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 物理学一般
Research InstitutionKitasato University

Principal Investigator

SOGO Kiyoshi  Kitasato University, School of Science, Associate Professor, 理学部, 助教授 (30265730)

Project Period (FY) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1998: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1997: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1996: ¥600,000 (Direct Cost: ¥600,000)
Keywordscompletely integrable systems / Cologero-Sutherland-Moser model / multi-variable orthogonal porynonials / Bogoyavlensky hierarchy / vertex operators / metastable state / relaxation process / saddle point solution / ソリトン理論 / ネマティック液晶 / 直交多項式 / Bogoyavlenskyモデル / 格子W代数 / ソリトン解 / ネマチック液晶 / フレデリックス転移 / Jack多項式 / 多変数Heroite多項式 / 多変数Legendre多項式
Research Abstract

(1) Two types of generalization of Calogero-Sutherland-Moser (CSM) Model are studied by changing the form of long-range potential. Exact. solutions of the eigenvalue problem (many body Schrodinger equation) are obtained. They are nothing but the multi-variable Hermite and Legendre polynomials. A simple formula is found to rive explicit forms of these multi-variable orthogonal polynomials.
(2) Bogoyavlensky hierarchy is studied, which is multi-componet generalization of Volterra model. This model is a completely integrable syatem and has a structure of the lattice W algebras. Vertex operator is constructed to generate multi-solition solutions.
(3) Stable state and metastable state are found for nematic liquid crystals in the magnetic field. These states are classified by the value W of winding number (topological invariant). Relaxation from metastable state to stable state is found to occur through the saddle point solution.

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] K. Sogo: "A Simple Derivation of Multivariable Hermite and Legendre Polynomials"Journal of Physical Society of Japan. 65・10. 3097-3099 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] k. Hikami, K. Sogo, R. Inoue: "Hidden Symmetry of the Bogoyavlensky Lattice. The Lattice W Algebras and the Vertex Operators"Journal of Physical Society of Japan. 66・12. 3756-3763 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K. Sogo, S.Ichimura: "Metastable State in Nematic Ligued Crystals under Magnetic Field"Journal of Physical Society of Japan. 67・9. 3026-3030 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K. Sogo: "A Simple Derivation of Multivariable Hermite and Legendre Polynomials"J. Phys. Soc. Jpn. 65 Vol. 10. 3097-3099 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K. Hihami, K. Sogo and R. Inoue: "Hidden Symmetry of the Bogoyavlensky Lattice. the Lattice W Alebras and the Vertex Operators"J. Phys. Soc. Jpn. 66 Vol. 12. 3756-3763 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K. Sogo and S. Ichimura: "Metastable State in Nematic Liquid Crystals under Magnetic Field"J. Phys. Soc. Jpn. 67 Vol. 9. 3026-3030 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kiyoshi SOGO and Shigeki ICHEMURA: "Metastable State in Nematic Liquid Crystals under Magnetic Field" Journal of the Physical Society of Japan. 67・9. 3026-3030 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kazuhiro HikAMi,Kiyoshi SoGo and Rei INoUE: "Hidden Symmetry of the Bogoyavlensky Lattice.the lattice W Algebras and Vertex Operators" Journal of the Physical Society of Japan. 66・12. 3756-3763 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kiyoshi SOGO: "A Simple Derivation of Multivariable Hermite and Legendre Polynominals" Journal of the Physical Society of Japan. 65・10. 3097-3099 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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