{
  "id": "1011.0708",
  "version": "v1",
  "published": "2010-11-02T19:29:20.000Z",
  "updated": "2010-11-02T19:29:20.000Z",
  "title": "New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces",
  "authors": [
    "Angel Ballesteros",
    "Alberto Enciso",
    "Francisco J. Herranz",
    "Orlando Ragnisco",
    "Danilo Riglioni"
  ],
  "comment": "13 pages; based in the contribution to the 28th International Colloquium on Group Theoretical Methods in Physics, Northumbria University (U.K.), 26-30th July 2010",
  "journal": "J.Phys.Conf.Ser.284:012011,2011",
  "doi": "10.1088/1742-6596/284/1/012011",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship between such Bertrand Hamiltonians and position-dependent mass systems is explicitly established. These results are illustrated through the example of a superintegrable (nonlinear) oscillator on a Bertrand-Darboux space, whose quantization and physical features are also briefly addressed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-02T19:29:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bertrands theorem",
      "superintegrable models",
      "position-dependent mass systems",
      "symmetric curved spaces",
      "bertrand hamiltonians"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics Conference Series",
      "year": 2011,
      "month": "Mar",
      "volume": 284,
      "number": 1,
      "pages": "012011"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 897272,
      "adsabs": "2011JPhCS.284a2011B"
    }
  }
}