SIGNATURES OF CHAOS IN QUANTUM BILLIARDS - MICROWAVE EXPERIMENTS

The signatures of classical chaos and the role of periodic orbits in t he wave-mechanical eigenvalue spectra of two-dimensional billiards are studied experimentally in microwave cavities. The survival probabilit y for all the chaotic cavity data shows a ''correlation hole,'' in agr eement with theory, that is absent for the integrable cavity. The spec tral rigidity Delta(3)(L), which is a measure of long-range correlatio n, is shown to be particularly sensitive to the presence of marginally stable periodic orbits. Agreement with random-matrix theory is achiev ed only after excluding such orbits, which we do by constructing a spe cial geometry, the Sinai stadium. Pseudointegrable geometries are also studied, and are found to display intermediate behavior.