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arXiv:1207.4696 [math.AP]AbstractReferencesReviewsResources

Eigenfunction statistics for a point scatterer on a three-dimensional torus

Nadav Yesha

Published 2012-07-19, updated 2012-12-19Version 3

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.

Comments: Revised according to referee's comments. Accepted for publication in Annales Henri Poincare
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