{
  "id": "1709.10403",
  "version": "v1",
  "published": "2017-09-27T16:33:46.000Z",
  "updated": "2017-09-27T16:33:46.000Z",
  "title": "Semiclassical catastrophe theory of simple bifurcations",
  "authors": [
    "A. G. Magner",
    "K. Arita"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.DS",
    "nlin.CD",
    "nucl-th"
  ],
  "abstract": "The Fedoriuk-Maslov catastrophe theory of caustics and turning points is extended for solving the bifurcation problems by the improved stationary phase method (ISPM). The trace formulas for the radial power-law (RPL) potentials are presented by the ISPM based on the second- and third-order expansion of the classical action near the stationary point. A considerable enhancement of contributions of the two orbits (pair of the parent and newborn ones) at their bifurcation is shown. The ISPM trace formula is proposed for a simple bifurcation scenario of Hamiltonian systems with continuous symmetries, where the contributions of the bifurcating parent orbits vanish as approaching the bifurcation point due to the reduction of the end-point manifold. This occurs since the contribution of the parent orbits is included into the term corresponding to the family of the new-born daughter orbits. Taking this feature into account, the ISPM level densities calculated for the RPL potential model are shown to be in good agreement with the quantum results at the bifurcations and asymptotically far from the bifurcation points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-27T16:33:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semiclassical catastrophe theory",
      "bifurcation point",
      "parent orbits",
      "rpl potential model",
      "stationary phase method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}