1988 Fiscal Year Final Research Report Summary
Validity of Soliton-Picture in Nonlinear Phenomena
| Project/Area Number |
61540271
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | University of Tokyo |
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Principal Investigator |
WADATI Miki College of Arts and Sciences, University of Tokyo, 教養学部, 助教授 (60015831)
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| Project Period (FY) |
1986 – 1988
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| Keywords | Soliton / Supercoiling DNA / Quantum Theory of Soliton / Quantum Inverse Scattering Method / Yang-Baxter Relation / Exactly Solvable Models in Statistical Mechanics / Knot Theory / 絡み目多項式 |
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| Research Abstract |
Based on the soliton theory and its generalizations, the following researches have been done.
1. One-dimensional elasticity is studied with both bending and torsion. Taking account of topological constraints for circular DNAs we obtain a macroscopic model for supercoiling DNAs.
2. Extending the soliton theory to quantum systems we can expl-ain how classical solitons arise from quantum solitons. The formulation is also useful to describe break-up of quantum soliton under external forces.
3. The quantum inverse scattering method yiels a unified frame-work to study exactly solvable models in dynamics and statis-tical mechanics. The key is the Yang-Baxter relation which is a sufficient condition for the solvability. By solving the Yang-baxter relation, we find that there exist at least solvable models in two-dimensional classical statis-tical mechanics.
4. A general method is found to derive link polynomial, topolo-gical invariant for knots and links, from an exactly solvable model in statistical mechanics. A set of new and powerful link polynomials, which includes the Jones polynomial as the simplest case, is found. Two-variable extensions and new algebras are also found.
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