Eigenfunction statistics for a point scatterer on a three-dimensional torus
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.
Keywords
Cite
@article{arxiv.1207.4696,
title = {Eigenfunction statistics for a point scatterer on a three-dimensional torus},
author = {Nadav Yesha},
journal= {arXiv preprint arXiv:1207.4696},
year = {2013}
}
Comments
Revised according to referee's comments. Accepted for publication in Annales Henri Poincare