{
  "id": "2212.13954",
  "version": "v1",
  "published": "2022-12-28T16:57:48.000Z",
  "updated": "2022-12-28T16:57:48.000Z",
  "title": "Comparing the spectrum of Schrödinger operators on quantum graphs",
  "authors": [
    "Patrizio Bifulco",
    "Joachim Kerner"
  ],
  "comment": "10 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We study Schr\\\"odinger operators on compact finite metric graphs subject to $\\delta$-coupling and standard boundary conditions. We compare the $n$-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the mean value of deviations. By doing this, we generalize recent results from Rudnick et al. obtained for domains in $\\mathbb{R}^2$ to the setting of quantum graphs. This also leads to a generalization of related results previously and independently obtained in [arXiv:2212.09143] and [arXiv:2212.12531] for metric graphs. In addition, based on our main result, we introduce some notions of circumference for a (quantum) graph which might prove useful in the future.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-28T16:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34L05",
      "81Q35",
      "34L15",
      "34L20"
    ],
    "keywords": [
      "quantum graphs",
      "schrödinger operators",
      "compact finite metric graphs subject",
      "standard boundary conditions",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}