{
  "id": "1205.0286",
  "version": "v2",
  "published": "2012-05-01T23:29:50.000Z",
  "updated": "2013-06-04T21:13:38.000Z",
  "title": "Quantum ergodic restriction for Cauchy data: Interior QUE and restricted QUE",
  "authors": [
    "Hans Christianson",
    "John Toth",
    "Steve Zelditch"
  ],
  "comment": "9 pages. Final version; incorporates referees' comments. To appear in MRL",
  "journal": "Math.Res.Lett 20 (2013) 465-475",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove a quantum ergodic restriction theorem for the Cauchy data of a sequence of quantum ergodic eigenfunctions on a hypersurface $H$ of a Riemannian manifold $(M, g)$. The technique of proof is to use a Rellich type identity to relate quantum ergodicity of Cauchy data on $H$ to quantum ergodicity of eigenfunctions on the global manifold $M$. This has the interesting consequence that if the eigenfunctions are quantum unique ergodic on the global manifold $M$, then the Cauchy data is automatically quantum unique ergodic on $H$ with respect to operators whose symbols vanish to order one on the glancing set of unit tangential directions to $H$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-04T21:13:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cauchy data",
      "global manifold",
      "quantum ergodic restriction theorem",
      "rellich type identity",
      "automatically quantum unique ergodic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0286C"
    }
  }
}