{
  "id": "2004.12931",
  "version": "v1",
  "published": "2020-04-27T16:44:34.000Z",
  "updated": "2020-04-27T16:44:34.000Z",
  "title": "A local test for global extrema in the dispersion relation of a periodic graph",
  "authors": [
    "Gregory Berkolaiko",
    "Yaiza Canzani",
    "Graham Cox",
    "Jeremy L. Marzuola"
  ],
  "comment": "29 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider a family of periodic tight-binding models (combinatorial graphs) that have the minimal number of links between copies of the fundamental domain. For this family we establish a local condition of second derivative type under which the critical points of the dispersion relation can be recognized as global maxima or minima. Under the additional assumption of time-reversal symmetry, we show that any local extremum of a dispersion band is in fact its global extremum if the dimension of the periodicity group is three or less, or (in any dimension) if the critical point in question is a symmetry point of the Floquet--Bloch family with respect to complex conjugation. We demonstrate that our results are nearly optimal with a number of examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-27T16:44:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "81Q35",
      "35Q40"
    ],
    "keywords": [
      "dispersion relation",
      "global extremum",
      "periodic graph",
      "local test",
      "critical point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}