{
  "id": "math-ph/0505081",
  "version": "v2",
  "published": "2005-05-30T15:27:21.000Z",
  "updated": "2005-08-08T13:35:58.000Z",
  "title": "Integrable potentials on spaces with curvature from quantum groups",
  "authors": [
    "Angel Ballesteros",
    "Francisco J. Herranz",
    "Orlando Ragnisco"
  ],
  "comment": "19 pages, 1 figure. Two references added",
  "journal": "J.Phys.A38:7129-7144,2005",
  "doi": "10.1088/0305-4470/38/32/004",
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "nlin.SI"
  ],
  "abstract": "A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson coalgebra. All these spaces have a non-constant curvature that depends on the deformation parameter z. As particular cases, the analogues of the harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed. Another deformed Hamiltonian is also shown to provide superintegrable systems on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant curvature that exactly coincides with z. According to each specific space, the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers. The non-deformed limit z=0 of all these Hamiltonians can then be regarded as the zero-curvature limit (contraction) which leads to the corresponding (super)integrable systems on the flat Euclidean and Minkowskian spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-08-08T13:35:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum groups",
      "integrable potentials",
      "sitter spaces",
      "central harmonic oscillator",
      "non-standard quantum deformation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 699645
    }
  }
}