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arXiv · 1207.4696

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

Nadav Yesha
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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.

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Nadav Yesha. 2012-12-19. Eigenfunction statistics for a point scatterer on a three-dimensional torus. https://doi.org/10.1007/s00023-013-0232-1

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