Statistical properties of spectra of pseudointegrable systems

Abstract

We analyze the spectral properties of various quantum pseudointegrable billiards (rhombus, gnomon, deltoid) and link them to the genus of the invariant surface of the corresponding classical model. Numerical investigations of the quantum billiards are completed by an experimental study of microwave resonators. Absorption spectra of microwaves in ``ssL-shaped'' resonators are measured and the distributions of eigenfrequencies are investigated.