{
  "id": "quant-ph/0604006",
  "version": "v1",
  "published": "2006-04-02T13:19:58.000Z",
  "updated": "2006-04-02T13:19:58.000Z",
  "title": "Regimes of stability of accelerator modes",
  "authors": [
    "Rebecca Hihinashvili",
    "Tali Oliker",
    "Yaniv S. Avizrats",
    "Alexander Iomin",
    "Shmuel Fishman",
    "Italo Guarneri"
  ],
  "comment": "Submitted to Physica D",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions in the phase diagrams, which are analogous to the Arnol'd tongues which have been extensively studied for a variety of dynamical systems, mostly dissipative ones. A rich variety of bifurcations of various types are observed, as well as period doubling cascades. Stability of periodic orbits is analyzed in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-02T13:19:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "accelerator modes",
      "periodic orbits",
      "phase diagram",
      "quantum dynamics",
      "cold atoms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}