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Quasi-Exactly Solvable Deformations of Gaudin Models and ``Quasi-Gaudin Algebras''

Alexander Ushveridze
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Abstract

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic Bethe ansatz solution only for some limited parts of the spectrum. An underlying algebra responsible for both the phenomena of complete integrability and quasi-exact solvability is constructed. We call it "quasi-Gaudin algebra" and demonstrate that it is a special non-Lie-algebraic deformation of the ordinary Gaudin algebra.

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Alexander Ushveridze. 1997-06-14. Quasi-Exactly Solvable Deformations of Gaudin Models and ``Quasi-Gaudin Algebras''. https://doi.org/10.1142/s0217732398000346

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