1998 Fiscal Year Final Research Report Summary
Algebraic Study of Compleetely Integrable Systems
| Project/Area Number |
08640512
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | Kitasato University |
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Principal Investigator |
SOGO Kiyoshi Kitasato University, School of Science, Associate Professor, 理学部, 助教授 (30265730)
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| Project Period (FY) |
1996 – 1998
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| Keywords | completely integrable systems / Cologero-Sutherland-Moser model / multi-variable orthogonal porynonials / Bogoyavlensky hierarchy / vertex operators / metastable state / relaxation process / saddle point solution |
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| 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.
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Research Products
(6 results)
