# Small scale equidistribution for a point scatterer on the torus

## TL;DR

This paper investigates how eigenfunctions of a point scatterer on flat tori distribute at small scales, establishing equidistribution results down to the Planck scale in two dimensions and at specific scales in three dimensions.

## Contribution

It provides new results on small scale equidistribution of eigenfunctions for point scatterers on flat tori, including the first such results at the Planck scale in 2D.

## Key findings

- Small scale equidistribution holds down to the Planck scale in 2D.
- In 3D, equidistribution is established at certain scales for all new eigenfunctions.
- The results extend understanding of quantum chaos and eigenfunction behavior on flat tori.

## 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.