{
  "id": "1409.6456",
  "version": "v1",
  "published": "2014-09-23T09:34:42.000Z",
  "updated": "2014-09-23T09:34:42.000Z",
  "title": "Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator",
  "authors": [
    "Eva-Maria Graefe",
    "Hans Jürgen Korsch",
    "Alexander Rush",
    "Roman Schubert"
  ],
  "comment": "12 pages, three figures",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the $PT$-symmetry is unbroken, i.e., the eigenvalues are purely real.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-23T09:34:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum dynamics",
      "swanson oscillator",
      "quantum wave functions",
      "non-hermitian quadratic oscillator",
      "symmetric model systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/48/5/055301",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2015,
      "month": "Feb",
      "volume": 48,
      "number": 5,
      "pages": "055301"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhA...48e5301G"
    }
  }
}