Eigenfunction Statistics for a Point Scatterer on a Three-Dimensional Torus

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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.

Original languageEnglish
Pages (from-to)1801-1836
Number of pages36
JournalAnnales Henri Poincare
Issue number7
StatePublished - Nov 2013
Externally publishedYes

Bibliographical note

Funding Information:
This work is part of the author’s M.Sc. thesis written under the supervision of Zeev Rudnick at Tel Aviv University. Partially supported by the Israel Science Foundation (grant No. 1083/10).

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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