{
  "id": "1612.02354",
  "version": "v1",
  "published": "2016-12-07T18:13:33.000Z",
  "updated": "2016-12-07T18:13:33.000Z",
  "title": "On the adiabatic theorem when eigenvalues dive into the continuum",
  "authors": [
    "Horia D. Cornean",
    "Arne Jensen",
    "Hans Konrad Knörr",
    "Gheorghe Nenciu"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian we study the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-07T18:13:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adiabatic theorem",
      "eigenvalues dive",
      "survival probability",
      "bound state vanishes",
      "dot energy varies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}