Quantum and wave dynamical chaos in superconducting microwave cavities: Billiards with singular scatterers and the 3D stadium

We study chaotic phenomena in 2D and 3D superconducting microwave resonators. The first example discussed is a flat resonator shaped as quarter of an ellipse with a perturbing antenna serving as an analog for a quantum billiard with a point-like scatterer. The system enables us to observe the intermediate, i.e. neither fully chaotic nor completely regular, level statistics of so-called pseudo-integrable systems. As a second example the trace formula of Balian and Duplantier for systems described by the vectorial Helmholtz equations is tested using a 3D stadium billiard. The exceptionally high Q-value of this resonator yields a complete eigenvalue spectrum of more than 18.000 levels up to 20 GHz forming the basis for the investigations of spectral properties.

Work supported by DFG under contract number Ri 242/16-3