Separation of Variables in BC-type Gaudin Magnet

Abstract

The integrable system is introduced based on the Poisson $rs$-matrix structure. This is a generalization of the Gaudin magnet, and in SL(2) case isomorphic to the generalized Neumann model. The separation of variables is discussed for both classical and quantum case.

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References in corpus (7)

• Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras
• Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
• Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem
• Separation of variables for the classical and quantum Neumann model
• Classical Functional Bethe Ansatz for $SL(N)$: separation of variables for the magnetic chain
• On Integrable Models Related to the $osp(1,2)$ Gaudin Algebra
• Quadrics on Complex Riemannian Spaces of Constant Curvature, Separation of Variables and the Gaudin Magnet

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• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Integrable Models From Twisted Half Loop Algebras
• Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
• Classical $N$-Reflection Equation and Gaudin Models
• Bäcklund Transformations for the Trigonometric Gaudin Magnet
• Relaxation of nonlinear oscillations in BCS superconductivity
• Coherent oscillations in superconducting cold Fermi atoms and their applications