{
  "id": "2106.16019",
  "version": "v1",
  "published": "2021-06-30T12:35:12.000Z",
  "updated": "2021-06-30T12:35:12.000Z",
  "title": "Kagome network with vertex coupling of a preferred orientation",
  "authors": [
    "Marzieh Baradaran",
    "Pavel Exner"
  ],
  "comment": "29 pages, 11 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP",
    "quant-ph"
  ],
  "abstract": "We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at the lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of infinite number of bands, some of which may be flat; the negative one has at most three and two bands, respectively. The kagome lattice example shows that even in graphs with such an uncommon vertex coupling spectral universality may hold: if its edges are incommensurate, the probability that a randomly chosen positive number is contained in the spectrum is $\\approx 0.639$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-30T12:35:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q35",
      "34L10"
    ],
    "keywords": [
      "kagome network",
      "preferred orientation",
      "uncommon vertex coupling spectral universality",
      "periodic quantum graphs",
      "kagome lattice example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}