Signatures of chaos in quantum billiards: Microwave experiments

Abstract

The signatures of classical chaos and the role of periodic orbits in the wave-mechanical eigenvalue spectra of two-dimensional billiards are studied experimentally in microwave cavities. The survival probability for all the chaotic cavity data shows a ``correlation hole,'' in agreement with theory, that is absent for the integrable cavity. The spectral rigidity ${\mathrm{\ensuremath{\Delta}}}_{3}$(L), which is a measure of long-range correlation, is shown to be particularly sensitive to the presence of marginally stable periodic orbits. Agreement with random-matrix theory is achieved only after excluding such orbits, which we do by constructing a special geometry, the Sinai stadium. Pseudointegrable geometries are also studied, and are found to display intermediate behavior.