Wave functions, nodal domains, flow, and vortices in open microwave systems

The signatures of wave functions in open cylindrical microwave billiards are investigated. The wave functions are obtained by means of a transmission measurement from an attached lead to a probe antenna inside the billiard. One can deduce complex wave functions and current densities of the system from the measurement. We investigate distributions and correlations of wave functions, currents and other quantities and compare this results with predictions from the random plane wave approach. Vortices and saddles are created and annihilated as a function of frequency and show a rich dynamic. Additionally we investigate nodal domains of the real and imaginary part of the wave function, their relation to the phase rigidity, and its parametric dependance on global phase shifts.