{
  "id": "2004.09137",
  "version": "v1",
  "published": "2020-04-20T09:00:36.000Z",
  "updated": "2020-04-20T09:00:36.000Z",
  "title": "Invariant graphs and spectral type of Schrödinger operators",
  "authors": [
    "Artur Avila",
    "Konstantin Khanin",
    "Martin Leguil"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DS",
    "math.SP"
  ],
  "abstract": "In this paper we study spectral properties of Schr\\\"odinger operators with quasi-periodic potentials related to quasi-periodic action minimizing trajectories for analytic twist maps. We prove that the spectrum contains a component of absolutely continuous spectrum provided that the corresponding trajectory of the twist map belongs to an analytic invariant curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-20T09:00:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J50"
    ],
    "keywords": [
      "spectral type",
      "invariant graphs",
      "schrödinger operators",
      "analytic invariant curve",
      "study spectral properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}