From Solitons to Knots and Links

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概要

• 論文の詳細を見る

• Development in the theory of solvable (integrable) models is reviewed. It covers from basic knowledge on completely integrable systems to recent work by the authors. First, soliton theory is briefly summarized. Through the inverse scattering method and its quantum extension, a central concept, commuting transfer matrices, and a key relation, the Yang-Baxter relation, are introduced. Second, it is shown that there exists at least ∞×∞ number of solvable models in two-dimensional statistical mechanics. Third, quantum spin chains corresponding to solvable statistical mechanical models are discussed. In particular, finite temperature extension of Baxter's formula is given. Fourth, a new approach is presented to the classification problem of knots and links. It is shown that link polynomial, topological invariant for knots and links, can be associated with any solvable model in statistical mechanics. In the presentation, universality of the soliton picture in field theory, spin systems and statistical mechanics is observed.

• 理論物理学刊行会の論文
• 1988-08-30

著者

• Wadati Miki

  Institue Of Applied Physics Tsukuba University

• AKUTSU Yasuhiro

  Institute of Physics, College of general Education University of Tokyo

• Akutsu Yasuhiro

  Institute Of Physics Kanagawa University

• Akutsu Yasuhiro

  Institute Of Physics College Of Arts And Sciences University Of Tokyo

• AKUTSU Yasuhiro

  Institute of Physics, College of Arts and Sciences University of Tokyo

関連論文

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• Envelope Solition in a New Nonlinear Transmission Line
• Experimental and Theoretical Study of the Recurrence Phenomena in Nonlinear Transmission Line
• A Loop Soliton Propagating along a Stretched Rope
• Classification of Exactly Solvable Two-Component Models
• Nonrelativistic Theory of Factorized S-Matrix
• Stiffening Transition in Vicinal Surfaces with Adsorption
• Knot Theory and Conformal Field Theory : Reduction Relations for Braid Generators
• Bethe States for the Quantum Three Wave Interaction Equation
• Nonlinear Transverse Oscillation of Elastic Beams under Tension
• The Kadomtsev-Petviashvili Equation:the Trace Method and the Soliton Resonances
• Quantum Three Wave Interaction Models
• Multiple-Pole Solutions of the Modified Korteweg-de Vries Equation
• New Factorized S-Matrix and Its Application to Exactly Solvable q-State Model. II
• New Factorized S-Matrix and Its Application to Exactly Solvable q-State Model. I
• Classical Soliton as a Limit of the Quantum Field Theory
• Two-Dimensional Tensor Product Variational Formulation
• Statistical Mechanics of Biomembrane Phase Transition.II.The First Order Transition with Pseudo-Critical Properties
• Statistical Mechanics of Biomembrane Phase Transition.I.Excluded VolumeEffects of Lipid Chains in Their Conformation Change
• First-Order Phase Transition in the S=1 Quantum Spin Chain with Partial Integrability
• Quasi-Reentrant Interface Behavior of Two-Dimensional Frustrated Ising Models
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• Analysis of the Equilibrium Crystal Shape by the Diagonal Terrace-Step-Kink Models with Non-SOS Type Steps
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