Exactly Solvable Models and Applications

精确可解模型和应用

• 批准号: 01540310
• 负责人: WADATI Miki
• 金额: $ 1.34万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540310/
• 关键词: Soliton; 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

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.

1）我们将孤子的理论扩展到对不稳定物理系统中非线性波的分析。引入了不稳定的非线性Schrodinger（UNL）方程，从而引入。解释了电子束等离子体中的局部模式。另外，新的非线性进化。提出了涵盖混乱和孤子现象的方程式。2）我们研究了外部噪声和辐射介质下的硫-N传播。使用具有辐射质量分布的一维晶格，我们阐明了局部波传播和平面波的调制。3）我们将巴克斯特公式扩展到将2-D统计机械模型和1-D Quatum System与有限温度案例相关联。将这种扩展与有限尺寸校正理论相结合，我们评估了量子自旋系统的自由能和covelation长度。4）我们开发了一种一般理论，以从二维统计力学中的准确可解决的模型中获取链路。应用理论。对于各种模型，我们获得了新的链接多项式和已知的链接多项式。该理论不仅在最近的数学物理学，而且在Quatum重力理论中也起着重要的作用。

项目成果

T.YAJIMA: "Soliton Solution and Its Property of Unstable Nonlinear Schro^^¨dinger Equation" J.Phys.Soc.Jpn.59. 41-47 (1990)

T.YAJIMA：“孤子解及其不稳定非线性 Schro^^dinger 方程的性质”J.Phys.Soc.Jpn.59 (1990)。

M.WADATI: "A New Hamiltonian Amplitude Equation Governing Modulated Wave Instability" J.Phys.Soc.Jpn.61. (1992)

M.WADATI：“控制调制波不稳定性的新哈密顿振幅方程”J.Phys.Soc.Jpn.61。

T.IIZUKA: "The RayleighーTaylor Instability and Nolinear Waves" J.Phys.Soc.Jpn.59. 3182-3193 (1990)

T.IIZUKA：“瑞利-泰勒不稳定性和非线性波”J.Phys.Soc.Jpn.59 (1990)。

T.IIZUKA: "Hydrogen Coverage on W(001)Surface as a Dynamical System" Journal of Physical Society of Japan. 58. 4329-4333 (1989)

T.IIZUKA：“作为动力系统的 W(001) 表面上的氢覆盖率”日本物理学会杂志。

M.WADATI: "Knot Theory and Conformal Field Theory,Reduction Relations for Braid Generators" Journal of Physical Society of Japan. 58. 1153-1161 (1989)

M.WADATI：“结理论和共形场论，辫状发生器的约简关系”日本物理学会杂志。