| Project/Area Number |
09044065
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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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 | The University of Tokyo |
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Principal Investigator |
WADATI Miki Graduate School of Science, University of Tokyo, Professor, 大学院・理学系研究科, 教授 (60015831)
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| Co-Investigator(Kenkyū-buntansha) |
KIMURA Yoshifumi Graduate School of Science, Nagoya University, Professor, 大学院・多元数理科学研究科, 教授 (70169944)
IIZUKA Takeshi Department of Physics, Ehime University, Research Associate, 理学部, 助手 (10263922)
HIKAMI Kazuhiro Graduate School of Science, University of Tokyo, Research Associate, 大学院・理学系研究科, 助手 (60262151)
YAJIMA Tetsu Information Science, Utsunomiya University, Associate Professor, 工学部, 助教授 (40230198)
DEGUCHI Tetsuo Graduate School of Humanities and Sciences, Ochanomizu University, Associate Professor, 大学院・人間文化研究科, 助教授 (70227544)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥11,100,000 (Direct Cost: ¥11,100,000)
Fiscal Year 1999: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1998: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1997: ¥3,800,000 (Direct Cost: ¥3,800,000)
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| Keywords | Soliton / Nonlinear dynamics / Discrete integrable system / Integrable system / Bose-Einstein Condenisation / Quantum integrable system / Instability / Geometrical model / 流体フィラメントの自由落下 / ブラック格子 / ギャップ・ソリトン / フェルミオン的R行列 / ソリトン方程式 / 離散的ソリトン方程式 / ソリトン・セルラーオートマトン / グロス・ピタエフスキー方程式 / ボース凝縮体の崩壊 / カイラル非線形シュレディンガー方程式 / デビィ・スチュワートソン方程式 / 量子カロジェロ模型 / 崩壊の臨界粒子数 / 非線形波動 / 多成分ソリトン方程式 / 光ソリトン / 可積分境界条件 / ボ-ズ・アインシュタイン凝縮 / 離散W代数 / 非対称排除過程模型 / 曲線短縮方程式 / 多次元非線形シュレディンガー方程式 |
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| Research Abstract |
1. For one-dimensional XXZ chain which is known to be quantum integrable spin system, scalar products and correlation functions of the asymmetric case, and spontaneous magnetization of the bounded case are calculated explicitly.
2. Static and dynamical properties of Bose-Einstein condensate under magnetic trap are investigated. Stability of D-dimensional nonlinear Schrodinger equation, stability of 2-component boson system, dynamics of boson-fermion system, and ground state and its stability of anisotropic condensate are analysed in detail.
3. An exact solution of the Navier-Stokes equations which describes a falling filament is found. The linear stability analysis of the solution gives a criterion for the pinch-off at the end points and the intermediate points.
4. Calogero model, Sutherland model and Ruijsenaars model are known as quantum integrable Particle systems. Their algebraic structures, integrabilities and orthogonal bases are clarified in a systematic way.
5. By extending the inverse scattering method, discrete multi-component soliton equations and their solutions are obtained. A new type of discrete multi-component nonlinear Schrodinger equation is also obtained.
6. For Volterra equation and Bogoyavlensky lattice, algebraic structures and integrabilities are clarified. Further, by discretizing time and dependent variables, integrable cellular automata are constructed.
7. A theory of fermionic R-matrix is developed to treat quantum integrable particle systems. This development enables us to study fermion systems without recourse to the Jordin-Wigner transformation. The integrable boundary problem can be treated as well.
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