**Authors: **Zeév Rudnick Henrik Ueberschär

**Publish Date**: 2012/08/24

**Volume:** 316, **Issue:** 3, **Pages:** 763-782

## Abstract

Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space In contrast when the classical dynamics is integrable there is concentration of eigenfunctions on invariant structures in phase space In this paper we study eigenfunction statistics for the Laplacian perturbed by a deltapotential also known as a point scatterer on a flat torus a popular model used to study the transition between integrability and chaos in quantum mechanics The eigenfunctions of this operator consist of eigenfunctions of the Laplacian which vanish at the scatterer and new or perturbed eigenfunctions We show that almost all of the perturbed eigenfunctions are uniformly distributed in configuration space

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