Pär Kurlberg: Quantum Ergodicity for point scatterers on arithmetic tori

Abstract: We investigate eigenfunctions of the Laplacian, perturbed by a delta-potential, on arithmetic 2D-tori. For a full density subsequence of "new" eigenfunction we prove decay of matric coefficients associated with pure momentum observables. This, together with previous work by Rudnich-Ueberschauer, allows us to conclude that quantum ergodicity holds for the set of "new" eigenfunctions.