{
  "id": "1403.4204",
  "version": "v2",
  "published": "2014-03-17T18:39:53.000Z",
  "updated": "2014-08-28T23:56:27.000Z",
  "title": "PT-symmetry breaking with divergent potentials: lattice and continuum cases",
  "authors": [
    "Yogesh N. Joglekar",
    "Derek D. Scott",
    "Avadh Saxena"
  ],
  "comment": "Revised text",
  "categories": [
    "quant-ph",
    "physics.optics"
  ],
  "abstract": "We investigate the parity- and time-reversal ($\\mathcal{PT}$)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, $\\mathcal{PT}$-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile $\\mathcal{PT}$ threshold for an open finite lattice, we show that continuum loss-gain potentials $V_\\alpha(x)\\propto i |x|^\\alpha \\mathrm{sign}(x)$ have a positive $\\mathcal{PT}$-breaking threshold for $\\alpha>-2$, and a zero threshold for $\\alpha\\leq -2$. When $\\alpha<0$ localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of $\\mathcal{PT}$-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the $\\mathcal{PT}$-symmetry broken region.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-17T18:39:53.000Z",
      "comment": "6 pages, 4 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-28T23:56:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.30.Er",
      "42.82.Et"
    ],
    "keywords": [
      "divergent potentials",
      "continuum cases",
      "pt-symmetry breaking",
      "symmetry broken region",
      "higher loss-gain strengths"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevA.90.032108",
      "journal": "Physical Review A",
      "year": 2014,
      "month": "Sep",
      "volume": 90,
      "number": 3,
      "pages": "032108"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvA..90c2108J"
    }
  }
}