RÉSUMÉ
We present detailed investigations of the experimental signatures of chaos-assisted tunneling in the two-dimensional annular billiard, as already summarized in Phys. Rev. Lett. 84, 867 (2000). We have performed analog experiments with two-dimensional, electromagnetic resonators allowing for a direct simulation of the corresponding quantum system. Spectra from a superconducting cavity with a high-frequency resolution are combined with electromagnetic intensity distributions of high spatial resolution experimentally determined using a normal conducting twin cavity. Thereby all eigenmodes were obtained with properly identified quantum numbers. Besides distributions of quasi-doublet splittings, which serve as fundamental observables for the tunneling between whispering gallery types of modes, we also focus on the distributions of resonance widths of the doublets. These directly reflect the role of lifetime of certain modes in the tunneling process. Here, as theoretically expected, the class of so-called beach modes is found to play a particular role in mediating between regular and chaotic states to enhance the tunneling strength. This behavior is found in the spectrum and also in the structure of the wave functions.
RÉSUMÉ
We report on first experimental signatures for chaos-assisted tunneling in a two-dimensional annular billiard. Measurements of microwave spectra from a superconducting cavity with high frequency resolution are combined with electromagnetic field distributions experimentally determined from a normal conducting twin cavity with high spatial resolution to resolve eigenmodes with properly identified quantum numbers. Distributions of quasidoublet splittings serve as basic observables for the tunneling between whispering gallery-type modes localized to congruent, but distinct tori which are coupled weakly to irregular eigenstates associated with the chaotic region in phase space.
RÉSUMÉ
We compare the statistical properties of eigenvalue sequences for a gamma=1 Bunimovich stadium billiard. The eigenvalues have been obtained in two ways: one set results from a measurement of the eigenfrequencies of a superconducting microwave resonator (real system), and the other set is calculated numerically (ideal system). We show influence of mechanical imperfections of the real system in the analysis of the spectral fluctuations and in the length spectra compared to the exact data of the ideal system. We also discuss the influence of a family of marginally stable orbits, the bouncing ball orbits, in two microwave stadium billiards with different geometrical dimensions.
RÉSUMÉ
The field distributions and eigenfrequencies of a microwave resonator which is composed of 20 identical cells have been measured. With external screws the periodicity of the cavity can be perturbed arbitrarily. If the perturbation is increased a transition from extended to localized field distributions is observed. For very large perturbations the field distributions show signatures of Anderson localization, while for smaller perturbations the field distribution is extended or weakly localized. The localization length of a strongly localized field distribution can be varied by adjusting the penetration depth of the screws. Shifts in the frequency spectrum of the resonator provide further evidence for Anderson localization.