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.
| Original language | English |
|---|---|
| Pages (from-to) | 1801-1836 |
| Number of pages | 36 |
| Journal | Annales Henri Poincare |
| Volume | 14 |
| Issue number | 7 |
| DOIs | |
| State | Published - Nov 2013 |
| Externally published | Yes |
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