{
  "id": "1703.03667",
  "version": "v1",
  "published": "2017-03-10T13:08:13.000Z",
  "updated": "2017-03-10T13:08:13.000Z",
  "title": "On the bound states of magnetic Laplacians on wedges",
  "authors": [
    "P. Exner",
    "V. Lotoreichik",
    "A. Pérez-Obiol"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP",
    "quant-ph"
  ],
  "abstract": "This note is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture $\\phi\\in (0,\\pi)$. So far, a proof was only obtained for the apertures $\\phi\\le \\pi/2$. The conviction in the validity of this conjecture for the apertures $\\phi\\in(\\pi/2,\\pi)$ mainly relied on numerical computations. In this note we succeed to prove existence of bound states for any aperture $\\phi \\lesssim 0.509\\pi$ using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a variational argument with numerical optimisation, we extend this interval up to any aperture $\\phi \\lesssim 0.595\\pi$. Moreover, we analyse the same question for closely related problems concerning magnetic Robin Laplacians on wedges and for magnetic Schr\\\"odinger operators in the plane with $\\delta$-interactions supported on broken lines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-10T13:08:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bound states",
      "magnetic laplacians",
      "related problems concerning magnetic",
      "problems concerning magnetic robin laplacians",
      "test functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}