{
  "id": "1207.4696",
  "version": "v3",
  "published": "2012-07-19T14:59:16.000Z",
  "updated": "2012-12-19T15:22:16.000Z",
  "title": "Eigenfunction statistics for a point scatterer on a three-dimensional torus",
  "authors": [
    "Nadav Yesha"
  ],
  "comment": "Revised according to referee's comments. Accepted for publication in Annales Henri Poincare",
  "doi": "10.1007/s00023-013-0232-1",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.NT",
    "nlin.CD"
  ],
  "abstract": "In this paper we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish at the scatterer, together with a set of new eigenfunctions (perturbed eigenfunctions). We first show that for a point scatterer on the standard torus all of the perturbed eigenfunctions are uniformly distributed in configuration space. Then we investigate the same problem for a point scatterer on a flat torus with some irrationality conditions, and show uniform distribution in configuration space for almost all of the perturbed eigenfunctions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-19T15:22:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "point scatterer",
      "three-dimensional torus",
      "perturbed eigenfunctions",
      "configuration space",
      "three-dimensional flat torus"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013AnHP...14.1801Y"
    }
  }
}