Thursday 26 Oct 2017: Scars for wave functions of a point scatterer on the torus
Steve Lester - Queen Mary University of London
A fundamental problem in Quantum Chaos is to understand the distribution of mass of Laplace eigenfunctions on a given smooth Riemannian manifold in the limit as the eigenvalue tends to infinity. In this talk I will consider a Laplace operator perturbed by a delta potential (point scatterer) on the torus and describe the distribution of mass of the eigenfunctions of this operator. It turns out that in this setting, the distribution of mass of the eigenfunctions is related to properties of integers which are representable as sums of two squares. I will describe this relationship and indicate how tools from analytic number theory such as sieve methods and the theory of multiplicative functions can be used to study the relevant properties of such integers.