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Mathematics > Analysis of PDEs

arXiv:1207.4696 (math)
[Submitted on 19 Jul 2012 (v1), last revised 19 Dec 2012 (this version, v3)]

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

Authors: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.
Comments: Revised according to referee's comments. Accepted for publication in Annales Henri Poincare
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Number Theory (math.NT); Chaotic Dynamics (nlin.CD)
Cite as: arXiv:1207.4696 [math.AP]
  (or arXiv:1207.4696v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1207.4696
Related DOI: https://doi.org/10.1007/s00023-013-0232-1

Submission history

From: Nadav Yesha [view email]
[v1] Thu, 19 Jul 2012 14:59:16 UTC (20 KB)
[v2] Thu, 30 Aug 2012 14:08:38 UTC (20 KB)
[v3] Wed, 19 Dec 2012 15:22:16 UTC (38 KB)
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