We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus. There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunctions which are eigenfunctions of the standard Laplacian, and new, perturbed eigenfunctions which are affected by the scatterers. We prove that along a density one sequence, the new eigenfunctions are uniformly distributed in configuration space, provided that the difference of the scattering points is Diophantine.
Cite this article
Nadav Yesha, Uniform distribution of eigenstates on a torus with two point scatterers. J. Spectr. Theory 8 (2018), no. 4, pp. 1509–1527DOI 10.4171/JST/233