"Number theory related to quantum chaos"
Abstract:Quantum chaos is concerned with properties of eigenvalues and eigenfunctions of "quantized Hamiltonians". For instance, can classical chaos be detected by looking at the spacings between eigenvalues? Another problem is if classical ergodicity forces eigenfunctions to be equidistributed in a certain sense. We will give a short introduction to quantized Hamiltonians, and then show that the study of the above mentioned questions for some simple dynamical systems gives rise to interesting problems in number theory.