Small Scale Equidistribution for a Point Scatterer on the Torus

Abstract

We study the small scale distribution of the eigenfunctions of a point scatterer (the Laplacian perturbed by a delta potential) on two-and three-dimensional flat tori. In two dimensions, we establish small scale equidistribution for the "new" eigenfunctions holding all the way down to the Planck scale. In three dimensions, small scale equidistribution is established for all of the "new" eigenfunctions at certain scales.