1991 Fiscal Year Final Research Report Summary
Exactly Solvable Models and Applications
| Project/Area Number |
01540310
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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 University of Tokyo Department of Physics Professor, 理学部, 教授 (60015831)
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| Project Period (FY) |
1989 – 1991
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| Keywords | Soliton / Yang-Baxter Relation / Exactly solvable Model / Unstable Nonlinear Schrodinger Equation / Knot Theory / Link Polynomial / Random Media / Finite Temperature Baxter's Formula |
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| 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.
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