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Separation of Variables in the Elliptic Gaudin Model

Evgueni K. Sklyanin, Takashi Takebe

arXiv:solv-int/9807008Communications in Mathematical PhysicsJul 1, 199926 citations

Elliptic Gaudin models and elliptic KZ equations

M. D. Gould, Yao-Zhong Zhang, Shao-you Zhao A

arXiv:nlin/0110038Nuclear Physics BMay 1, 200217 citations

Separation of variables in the Gaudin model

Evgeny Konstantinovich Sklyanin

Journal of Mathematical SciencesOct 1, 1989275 citations

Separation of variables and the XXZ Gaudin magnet

Ernest G. Kalnins, Vadim B. Kuznetsov, Willard Miller

In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case of linear r-matrix algebra which corresponds to the trigonometric 4x4 r-matrix (of the XXZ type). We comment also on the corresponding problem for the elliptic (XYZ) r-matrix. A prescription for obtaining integrable systems associated with multiple poles of an L-operator is given.

arXiv:hep-th/9412190Dec 21, 19944 citations

Separation of variables and XXZ Gaudin magnet

Ernest G. Kalnins, Vadim B. Kuznetsov, Willard Miller

Abstract. In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case of linear r-matrix algebra which corresponds to the trigonometric 4 × 4 r-matrix (of the XXZ type). We comment also on the corresponding problem for the elliptic (XYZ) r-matrix. A prescription for obtaining integrable systems associated with multiple poles of an L-operator is given. 1. Introduction. Separation of variables for the Hamilton-Jacobi and Schrödinger equations have long been known as methods for explicit solution of these equations in appropriate circumstances. The technical requirements for this method of solution have quite fully developed in recent years (see [1–8]). In particular the relationship between the separable systems and the Gaudin magnet [4,9] integrableAbstract. In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case of linear r-matrix algebra which corresponds to the trigonometric 4 × 4 r-matrix (of the XXZ type). We comment also on the corresponding problem for the elliptic (XYZ) r-matrix. A prescription for obtaining integrable systems associated with multiple poles of an L-operator is given. 1. Introduction. Separation of variables for the Hamilton-Jacobi and Schrödinger equations have long been known as methods for explicit solution of these equations in appropriate circumstances. The technical requirements for this method of solution have quite fully developed in recent years (see [1–8]). In particular the relationship between the separable systems and the Gaudin magnet [4,9] integrable

Jan 1, 19952 citations

Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field

T. Skrypnyk

Abstract We study the problem of separation of variables for classical integrable Hamiltonian systems governed by non-skew-symmetric non-dynamical s o ( 3 ) ⊗ s o ( 3 ) -valued elliptic r -matrices with spectral parameters. We consider several examples of such models, and perform separation of variables for classical anisotropic one- and two-spin Gaudin-type models in an external magnetic field, and for Jaynes–Cummings–Dicke-type models without the rotating wave approximation.

Journal of Physics A Mathematical and TheoreticalJun 6, 201711 citations

Separation of variables, K-twisted elliptic r-matrix and elliptic Gaudin-type model

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