Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed scatterers, each mimicking an $r^{-2}$ repulsive potential. Analysis of both stationary wave fields and transient transport shows large
deviations from Rayleighs law for the wave height distribution, which can only partially be described by existing multiple-scattering theories. At high frequencies, the flow shows branching structures similar to those observed previously in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are likely to be responsible for the observed structures. Particular conspicuous features observed in the stationary patterns are hot spots with intensities far beyond those expected in a random wave field. Reinterpreting the flow patterns as ocean waves in the presence of spatially varying currents or depth variations in the sea floor, the branches and hot spots lead to enhanced frequency of freak or rogue wave formation in these regions.
From the measurement of a reflection spectrum of an open microwave cavity the poles of the scattering matrix in the complex plane have been determined. The resonances have been extracted by means of the harmonic inversion method. By this it became po
ssible to resolve the resonances in a regime where the line widths exceed the mean level spacing up to a factor of 10, a value inaccessible in experiments up to now. The obtained experimental distributions of line widths were found to be in perfect agreement with predictions from random matrix theory when wall absorption and fluctuations caused by couplings to additional channels are considered.
From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can b
e considered as {em local} since wave functions are influenced only locally, in contrast to, e. g., the situation where the fidelity decay is caused by the shift of one billiard wall. Using the random-plane-wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic $1/t$ decay for long times. A perfect agreement between experiment and theory has been found, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities.
The theoretical interpretation of measurements of wavefunctions and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of th
e antenna, we describe antennas as point-like perturbations. This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of wavefunction measurements. This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce ``renormalized Green function, which contains the information on boundary reflections and has no singularity inside the cavity.
