Superintegrable anharmonic oscillators on N-dimensional curved spaces
Abstract
The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family of quasi-maximally superintegrable perturbations of the intrinsic oscillator on such spaces. Moreover, the generalization of this construction to those N-dimensional spaces with non-constant curvature that are endowed with sl(2)-coalgebra symmetry is presented. As the first examples of the latter class of systems, both the oscillator potential on an N-dimensional Darboux space as well as several families of its quasi-maximally superintegrable anharmonic perturbations are explicitly constructed.
Cite
@article{arxiv.0710.0843,
title = {Superintegrable anharmonic oscillators on N-dimensional curved spaces},
author = {Angel Ballesteros and Alberto Encisco and Francisco J. Herranz and Orlando Ragnisco},
journal= {arXiv preprint arXiv:0710.0843},
year = {2015}
}
Comments
10 pages. Based on the contribution presented at the "17th Conference on Nonlinear Evolution Equations and Dynamical Systems" NEEDS 2007. L'Ametlla de Mar, Spain, June 17-24, 2007. Minor changes and two references added. To appear in J. Nonlinear Math. Phys