{
  "id": "1702.03811",
  "version": "v1",
  "published": "2017-02-13T15:20:59.000Z",
  "updated": "2017-02-13T15:20:59.000Z",
  "title": "Behavior of eigenvalues in a region of broken-PT symmetry",
  "authors": [
    "Carl M. Bender",
    "Nima Hassanpour",
    "Daniel W. Hook",
    "S. P. Klevansky",
    "Christoph Sünderhauf",
    "Zichao Wen"
  ],
  "comment": "14 pages, 19 figures",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "PT-symmetric quantum mechanics began with a study of the Hamiltonian $H=p^2+x^2(ix)^\\varepsilon$. When $\\varepsilon\\geq0$, the eigenvalues of this non-Hermitian Hamiltonian are discrete, real, and positive. This portion of parameter space is known as the region of unbroken PT symmetry. In the region of broken PT symmetry $\\varepsilon<0$ only a finite number of eigenvalues are real and the remaining eigenvalues appear as complex-conjugate pairs. The region of unbroken PT symmetry has been studied but the region of broken PT symmetry has thus far been unexplored. This paper presents a detailed numerical and analytical examination of the behavior of the eigenvalues for $-4<\\varepsilon<0$. In particular, it reports the discovery of an infinite-order exceptional point at $\\varepsilon=-1$, a transition from a discrete spectrum to a partially continuous spectrum at $\\varepsilon=-2$, a transition at the Coulomb value $\\varepsilon=-3$, and the behavior of the eigenvalues as $\\varepsilon$ approaches the conformal limit $\\varepsilon=-4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-13T15:20:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eigenvalues",
      "broken-pt symmetry",
      "unbroken pt symmetry",
      "pt-symmetric quantum mechanics began",
      "infinite-order exceptional point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}