{
  "id": "1403.5798",
  "version": "v1",
  "published": "2014-03-23T20:35:07.000Z",
  "updated": "2014-03-23T20:35:07.000Z",
  "title": "Spectral asymptotics for $δ'$ interaction supported by a infinite curve",
  "authors": [
    "Michal Jex"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP",
    "quant-ph"
  ],
  "abstract": "We consider a generalized Schr\\\"odinger operator in $L^2(\\mathbb R^2)$ describing an attractive $\\delta'$ interaction in a strong coupling limit. $\\delta'$ interaction is characterized by a coupling parameter $\\beta$ and it is supported by a $C^4$-smooth infinite asymptotically straight curve $\\Gamma$ without self-intersections. It is shown that in the strong coupling limit, $\\beta\\to 0_+$, the eigenvalues for a non-straight curve behave as $-\\frac{4}{\\beta^2} +\\mu_j+\\mathcal O(\\beta|\\ln\\beta|)$, where $\\mu_j$ is the $j$-th eigenvalue of the Schr\\\"odinger operator on $L^2(\\mathbb R)$ with the potential $-\\frac14 \\gamma^2$ where $\\gamma$ is the signed curvature of $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-23T20:35:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral asymptotics",
      "infinite curve",
      "interaction",
      "strong coupling limit",
      "smooth infinite asymptotically straight curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5798J"
    }
  }
}