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Annales Henri Poincaré

, Volume 16, Issue 1, pp 1–14 | Cite as

Quantum Ergodicity for a Point Scatterer on the Three-Dimensional Torus

  • Nadav YeshaEmail author
Article

Abstract

Consider a point scatterer (the Laplacian perturbed by a delta-potential) on the standard three-dimensional flat torus. Together with the eigenfunctions of the Laplacian which vanish at the point, this operator has a set of new, perturbed eigenfunctions. In a recent paper, the author was able to show that all of the perturbed eigenfunctions are uniformly distributed in configuration space. In this paper we prove that almost all of these eigenfunctions are uniformly distributed in phase space, i.e. we prove quantum ergodicity for the subspace of the perturbed eigenfunctions. An analogue result for a point scatterer on the two-dimensional torus was recently proved by Kurlberg and Ueberschär.

Keywords

Point Scatterer Unperturbed Problem Quantum Ergodicity Integer Lattice Point Standard Basis Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Raymond and Beverly Sackler School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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