{
  "id": "1804.05620",
  "version": "v1",
  "published": "2018-04-16T11:45:45.000Z",
  "updated": "2018-04-16T11:45:45.000Z",
  "title": "Instability of resonances under Stark perturbations",
  "authors": [
    "Arne Jensen",
    "Kenji Yajima"
  ],
  "comment": "11 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Let $H^{\\varepsilon}=-\\frac{d^2}{dx^2}+\\varepsilon x +V$, $\\varepsilon\\geq0$, on $L^2(\\mathbf{R})$. Let $V=\\sum_{k=1}^Nc_k|\\psi_k\\rangle\\langle\\psi_k|$ be a rank $N$ operator, where the $\\psi_k\\in L^2(\\mathbf{R})$ are real, compactly supported, and even. Resonances are defined using analytic scattering theory. The main result is that if $\\zeta_n$, ${\\rm Im}\\zeta_n<0$, are resonances of $H^{\\varepsilon_n}$ for a sequence $\\varepsilon_n\\downarrow0$ as $n\\to\\infty$ and $\\zeta_n\\to\\zeta_0$ as $n\\to\\infty$, ${\\rm Im}\\zeta_0<0$, then $\\zeta_0$ is \\emph{not} a resonance of $H^0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-16T11:45:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V10",
      "35J10",
      "35P05",
      "35P25"
    ],
    "keywords": [
      "stark perturbations",
      "instability",
      "analytic scattering theory",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}