Integrable deformations of oscillator chains from quantum algebras

Details Integrable deformations of oscillator chains from quantum algebras Integrable deformations of oscillator chains from quantum algebras

1999-11-03

arxiv.org/abs/solv-int/9911004v1

J. Phys. A, 32 (1999) 8851-8862

Mathematics

Quantum Algebra

15 pages, LaTeX

Scientific paper

10.1088/0305-4470/32/50/306

A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions for all the associated integrals of motion are given, and the long-range nature of the interactions introduced by the deformation is shown to be linked to the underlying coalgebra structure. Separability and superintegrability properties of such systems are analysed, and their connection with classical angular momentum chains is used to construct a non-standard integrable deformation of the XXX hyperbolic Gaudin system.

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