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Quantum inverse scattering method and Yang-Baxter relation for integrable spin systems
Nonlinear science abstracts
423
spatially. This mechanism is effective to the onset of the chaos both for energy conserved and non-conserved perturbation. JOURNAL: Submitted to J. Phys. Soc. Jpn. 423
(P8,TI) QUANTUM INVERSE SCATTERING METHOD AND YANG-BAXTER RELATION FOR INTEGRABLE SPIN SYSTEMS, Kiyoshi Sogo and Miki Wadati, Institute of Physics, University of Tokyo, Komaba, Tokyo 153, JAPAN. The Lax pair for spin 1/2 Heisenberg XYZ model is presented. This gives a basis for the quantum inverse scattering method. A generalization of the Yang-Baxter relation to arbitrary spin is presented through the factorized Smatrix theory. An equivalent vertex model is solved exactly by the quantum inverse scattering method. JOURNAL: Progress of Theoretical Physics, 6 8 1, (1982) 424
(P8,TI) CLASSIFICATION OF EXACTLY SOLVABLE TWO-COMPONENT MODELS, Kiyoshi Sogo, Mamoru Uchinami, Yasuhiro Akutsu and Miki Wadati, Institute of Physics, College of General Education, University of Tokyo, Komaba, Tokyo 153, JAPAN. In the case of two-component models, all possible solutions for factorization equations of S-matrix are obtained. These solutions give a classification ofsolvable vertex models. It is found that Yang-Baxter relation is more general than the factorization equaion. The six vertex model by Yang, Yang and Sutherland is derived not from the factorization equation but from YangBaxter relation. Thus it is concluded that Yang-Baxter relation lies at the basis of all the known solvable two component models. Furthermore, spin Hamiltonians corresponding to our vertex models are presented in explicit forms. JOURNAL: Progress of Theoretical Physics, 68 2 (1982) 425
(M2,T1) GENERAL SOLUTION AND LAX PAIR FOR I-D CLASSICAL MASSELSS THIRRING MODEL, Miki Wadati, Institute of Physics, College of General Education, Univeristy of Tokyo, Komaba 3-8-1, Tokyo 153, JAPAN. Classical massless Thirring model in one dimensional space is studied. General solution and Lax pair are explicitly presented. Both results imply that the system is completely integrable. JOURNAL: none given
426
(M1,I4) CASCADE OF PERIOD DOUBLINGS OF TORI, A. Arneodo, Laboratoire de Physique Th~orique, Universit~de Nice 06034 Nice Cedex, FRANCE; P. H. Coullet, CNRS, M~canique Statistique, Universit~ de Nice 06034 Nice Cedex, FRANCE; E. A. Spiegel, Astronomy Department, Columbia University, New York, NY 10027, USA. We propose a three-dimensional map to model the effects of periodic forcing on a system displaying a transition to chaos through a cascade of perioddoubling bifurcations. JOURNAL: none given
427
(P8,W3) ASYMPTOTIC CALCULATION OF SOLITON MASSES, E. B. Bogomolny, V. A. Fateev, The Academy of Sciences of the USSR, L. D. Landau Institute for Theoretical Physics, USSR. The leading terms of the mass asymptotics of a sphericallysymmetric soliton of a four-dimensional chiral Skyrme model have been calculated. We found that E N = 8.310 N(N + 0.8726)/2 + 0(i) at large topological
423
spatially. This mechanism is effective to the onset of the chaos both for energy conserved and non-conserved perturbation. JOURNAL: Submitted to J. Phys. Soc. Jpn. 423
(P8,TI) QUANTUM INVERSE SCATTERING METHOD AND YANG-BAXTER RELATION FOR INTEGRABLE SPIN SYSTEMS, Kiyoshi Sogo and Miki Wadati, Institute of Physics, University of Tokyo, Komaba, Tokyo 153, JAPAN. The Lax pair for spin 1/2 Heisenberg XYZ model is presented. This gives a basis for the quantum inverse scattering method. A generalization of the Yang-Baxter relation to arbitrary spin is presented through the factorized Smatrix theory. An equivalent vertex model is solved exactly by the quantum inverse scattering method. JOURNAL: Progress of Theoretical Physics, 6 8 1, (1982) 424
(P8,TI) CLASSIFICATION OF EXACTLY SOLVABLE TWO-COMPONENT MODELS, Kiyoshi Sogo, Mamoru Uchinami, Yasuhiro Akutsu and Miki Wadati, Institute of Physics, College of General Education, University of Tokyo, Komaba, Tokyo 153, JAPAN. In the case of two-component models, all possible solutions for factorization equations of S-matrix are obtained. These solutions give a classification ofsolvable vertex models. It is found that Yang-Baxter relation is more general than the factorization equaion. The six vertex model by Yang, Yang and Sutherland is derived not from the factorization equation but from YangBaxter relation. Thus it is concluded that Yang-Baxter relation lies at the basis of all the known solvable two component models. Furthermore, spin Hamiltonians corresponding to our vertex models are presented in explicit forms. JOURNAL: Progress of Theoretical Physics, 68 2 (1982) 425
(M2,T1) GENERAL SOLUTION AND LAX PAIR FOR I-D CLASSICAL MASSELSS THIRRING MODEL, Miki Wadati, Institute of Physics, College of General Education, Univeristy of Tokyo, Komaba 3-8-1, Tokyo 153, JAPAN. Classical massless Thirring model in one dimensional space is studied. General solution and Lax pair are explicitly presented. Both results imply that the system is completely integrable. JOURNAL: none given
426
(M1,I4) CASCADE OF PERIOD DOUBLINGS OF TORI, A. Arneodo, Laboratoire de Physique Th~orique, Universit~de Nice 06034 Nice Cedex, FRANCE; P. H. Coullet, CNRS, M~canique Statistique, Universit~ de Nice 06034 Nice Cedex, FRANCE; E. A. Spiegel, Astronomy Department, Columbia University, New York, NY 10027, USA. We propose a three-dimensional map to model the effects of periodic forcing on a system displaying a transition to chaos through a cascade of perioddoubling bifurcations. JOURNAL: none given
427
(P8,W3) ASYMPTOTIC CALCULATION OF SOLITON MASSES, E. B. Bogomolny, V. A. Fateev, The Academy of Sciences of the USSR, L. D. Landau Institute for Theoretical Physics, USSR. The leading terms of the mass asymptotics of a sphericallysymmetric soliton of a four-dimensional chiral Skyrme model have been calculated. We found that E N = 8.310 N(N + 0.8726)/2 + 0(i) at large topological