{
  "id": "1505.04945",
  "version": "v1",
  "published": "2015-05-19T10:28:50.000Z",
  "updated": "2015-05-19T10:28:50.000Z",
  "title": "Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds",
  "authors": [
    "Fabricio Macià",
    "Gabriel Rivière"
  ],
  "comment": "36 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We study the long time dynamics of the Schr\\\"odinger equation on Zoll manifolds. We establish criteria under which the solutions of the Schr\\\"odinger equation can or cannot concentrate on a given closed geodesic. As an application, we derive some results on the set of semiclassical measures for eigenfunctions of Schr\\\"odinger operators: we prove that adding a potential to the Laplacian on the sphere results on the existence of geodesics $\\gamma$ such that $\\delta_\\gamma$ cannot be obtained as a semiclassical measure for some sequence of eigenfunctions. We also show that the same phenomenon occurs for the free Laplacian on certain Zoll surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T10:28:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zoll manifolds",
      "schrödinger evolution",
      "non-concentration",
      "long time dynamics",
      "semiclassical measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504945M"
    }
  }
}