Henrik Ueberschär

On the random wave conjecture for Seba's billiard

Berry's random wave conjecture asserts that the eigenfunctions of quantum billiards whose classical dynamics is chaotic should behave like random superpositions of plane waves in the limit as frequency tends to infinity. We will discuss the validity of this conjecture for Seba's billiard, a singular quantum billiard which belongs to the class of pseudo-integrable systems. We explain why the conjecture fails for the case of diophatine tori. We will also discuss the interesting case of arithmetic tori. This talk is based on recent work with Pär Kurlberg.