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Exactly Solvable Models and Applications

Research Project

Project/Area Number 01540310
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 物理学一般
Research InstitutionUniversity of Tokyo

Principal Investigator

WADATI Miki  University of Tokyo Department of Physics Professor, 理学部, 教授 (60015831)

Project Period (FY) 1989 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1991: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1990: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1989: ¥700,000 (Direct Cost: ¥700,000)
KeywordsSoliton / Yang-Baxter Relation / Exactly solvable Model / Unstable Nonlinear Schrodinger Equation / Knot Theory / Link Polynomial / Random Media / Finite Temperature Baxter's Formula / 不安定非線形シュレディンガ-方程式 / 逆散乱法 / ランダム行列 / 不安定シュレディンガ-方程式 / ランダム性と非線形性 / 組みひも群 / 可解模型 / 共形場理論 / 吸着脱離過程
Research Abstract

1) We extend the theory of soliton to the analysis of non-linear waves in unstable physical system. The unstable Nonlinear Schrodinger (UNLS) equation is introduced, whereby propagation of. a localized mode in electron-beam plasma is explained. In addition, a new nonlinear evolution. equation which encompass chaos and soliton phenomena is proposed.
2) We investigate the solillo-n propagations under external noise and in radom media. Using a one-dimensional lattice with radom mass distribution, we clarify the localized wave propagations and the modulations of plane waves.
3) We extend the Baxter's formula which relates 2-D statistical mechanical model and 1-D quatum system into finite temperature case. Combining this extension with the theory of finite size corrections, we evaluate the free energies and the covelation lengths of quantum spin systems.
4) We develop a general theory to obtain link polgnomials from exactly solvable models in 2-D statistical mechanics. Applying the theory. to various model, we get new link polynomials and the known link polynomials. This theory may play an important role not only in recent mathematical' physics but also in quatum gravitation theory.

Report

(4 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • 1989 Annual Research Report
  • Research Products

    (42 results)

All Other

All Publications (42 results)

  • [Publications] M.WADATI: "Old and New Link Polynomials from the Theory of Exactly Solvable Models" Physica D. 51. 376-387 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.WADATI: "Solition Phenomana in Unstable Media" Physica D. 51. 388-406 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.WADATI: "The Unstable Nonlinear Schrodinger Equation;The Theory and its Applications" Chaos,Solition and Fractal. 1. 149-271 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.IIZUKA: "Propagation of Solitons in Random Lattices" J.Phys.Soc.Jpn.60. 4167-4174 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.WADATI: "A New Hamiltonian Ampletude Equation Governing Modulated Wave Instability" J.Phys.Soc.Jpn.61. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] J.SUZUKI: "Exactiy Solvable Models and Finite Size Corrections" International Modern Physics. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.WADATI: "Proceedings of the 25th International Conference on High Energy Physics,Vol.2,pp.1389-1398" World Scientific Publishing ed.by K.K.Phua and Y.Yamaguchi, 11 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.IIZUKA: "Nonlinear Dispersive Waves" World Scientific Publising ed.by L.Debnath, (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Wadati and T. Deguchi: "Old and New Link Polynomials from the Theory of Exactly solvable Models" Physica D. 51. 376-387 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Wadati, T. Iizuka and T. Yajima: "Soliton Phenomena in Unstable Media" Physica D. 51. 388-406 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Wadati: "Deformation of solitons in Random Media" J. Phys. Soc. Jpn.59. 4201-4203 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Iizuka, M. Wadati and T. Yajima: "the Unstable Schrodinger Equation and Dark Solitons" J. Phys. Soc. Jpn.60. 2862-2875 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Mori, K. Kaneko and M. Wadati: "Fracture Dynamics by Quenching. I. Crack Patterns" J. Phys. Soc. Jpn.60. 1591-1599 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Iizuka, T. Nakao and M. wadati: "Propagation of solitons in Random Lattices" J. Phys. Soc. Jpn.60. 4167-4174 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Wadati, T. Yajima and T. Iizuka: "The Unstable Nonlinear Schrodinger Equation, The Theory and its Applications" Chaos, Soliton and Fractal. 1. 249-271 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Wadati, H. Segur and M. J. Ablowitz: "A New Hamiltonian Amplitude Equation Governing Modulated Wave Instability]" J. Phys. Soc. Jpn.61. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] J. Suzuki, T. Nagao and M. Wadati: "Exactly Solvable Models and Finite Size Corrections" International Modern Physics. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.WADATI: "Old and New Link Polynomials from the Theory of Exactly Solvable Models" Physica D. 51. 376-387 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.WADATI: "Soliton Phenomena in Unstable Media" Physica D. 51. 388-406 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.WADATI: "The Unstable Nonlinear Schrodinger Equation; The Theory and its Applications" Chaos,Soliton and Fractal. 1. 249-271 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.IIZUKA: "Propagation of Solitons in Random Lattices" J.Phys.Soc.Jpn.60. 4167-4174 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.WADATI: "A New Hamiltonian Amplitude Equation Governing Modulated Wave Instability" J.Phys.Soc.Jpn.61. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] J.SUZUKI: "Exactly Solvable Models and Finite Size Corrections" International Modern Physics. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] ed.by K.K.Phua and Y.Yamaguchi,M.WADATI: "Proceedings of the 25th International Conference on High Energy Physics,Vol.2" World Scientific Publishing, 11 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] ed.by L.Debnath,T.IIZUKA: "Nonlinear Dispersive Waves" World Scientific Publishing, (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.YAJIMA: "Soliton Solution and Its Property of Unstable Nonlinear Schro^^¨dinger Equation" J.Phys.Soc.Jpn.59. 41-47 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.IIZUKA: "The RayleighーTaylor Instability and Nolinear Waves" J.Phys.Soc.Jpn.59. 3182-3193 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] J.SUZUKI: "A New Approach to Quantum Spin Chains at Finite Temperature" J.Phys.Soc.Jpn.59. 2667-2680 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.YAJIMA: "Solitons in Electron Beam Plasma" J.Phys.Soc.Jpn.59. 3237-3248 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.WADATI: "Deformation of Solitons in Random Media" J.Phys.Soc.Jpn.59. 4201-4203 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.WADATI: "Old and New Link Polynomials from the Theory of Exactly Solvable Models" Physica D.

    • Related Report
      1990 Annual Research Report
  • [Publications] M.WADATI: "Soliton Phenomena in Unstable Media" Physica D.

    • Related Report
      1990 Annual Research Report
  • [Publications] M.WADATI: "Unstable Nonlinear Schro^^¨dinger Equation : The Theory and its Application" Chaos,Solitons and Fractals.

    • Related Report
      1990 Annual Research Report
  • [Publications] T.DEGUCHI: "Graded Solutions of the YangーBaxter Relation and Link Polynomials" J.Phys.A : Math.Gen.23. 1861-1875 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.WADATI: "Lecture Notes in Mathematics ed.Gu Chaohao" SpringerーVerlag, 25 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.YAJIMA: "Integrable and Superintegrable Systems ed.B.A.Kuperschmidt" World Scientific, 20 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.WADATI: "Knot Theory and Conformal Field Theory,Reduction Relations for Braid Generators" Journal of Physical Society of Japan. 58. 1153-1161 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.IIZUKA: "Hydrogen Coverage on W(001)Surface as a Dynamical System" Journal of Physical Society of Japan. 58. 4329-4333 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] M.WADATI: "Exactly Solvable Models and Knot Theory" Physics Reports. 180. 247-332 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.DEGUCHI: "Knot Theroy Based on Solvable Models at Criticality" Advanced Studies in Mathematics. 19. 193-285 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.YAJIMA: "Soliton Solution and Its Property of Unstable Nonlinear Schro^¨dinger Equation" Journal of Physical Society of Japan. 59. 41-47 (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] Y.AKUTSU: "Braid Group, Knot Theory and Statistical Mechanics,ed.by C.N.Yang and M.L.Ge" World Scientific Publishing, 50 (1989)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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