# Research Topics

### Current and vortex statistics in microwave billiards

Using the one-to-one correspondence between the Poynting vector in a microwave billiard and the probability current density in the corresponding quantum system probability densities and currents were studied in a microwave billiard with a ferrite insert as well as in an open billiard. Distribution functions were obtained for probability densities, currents and vorticities. In addition the vortex pair correlation function could be extracted. For all studied quantities a complete agreement with the predictions from the random-superposition-of-plane-wave approach was obtained.

### Resonance Trapping

The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. We performed the first direct experimental verification of this effect, known as resonance trapping. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.

### Transmission through chaotic billiards

There are numerous theoretical results on transmission properties through chaotic systems from random matrix theory. In particular there are predictions on the fluctuation properties of the transmission in dependence of the number of incoming and outgoing channels. Apart from some results for real mesoscopic billiards, there are as yet no experiments available. This is our motivation to study the transmission of microwaves through a billiard in dependence of the number of incoming and outgoing channels.

### Eigenvalue dynamics by variation of an external parameter

Level dynamics
measurements have been performed in a Sinai microwave billiard as a
function of one length, as well as in rectangular billiards with
randomly distributed disks as a function of the position of one of the
disks. In the first case, where the shift of the wall changes the field
distribution *globally*, velocity distributions and
autocorrelation functions are well described by universal functions
derived by Simons and Altshuler. The universality breaks down for the
second type of level dynamics, where the shift of one disk changes the
field distribution only *locally*. Here another type of
universal correlations is observed which can be derived under the
assumption that in chaotic billiards the wave functions may be
described by a random superposition of plane waves.

### Experimental verification of topologically induced vortices

Using flat electromagnetic resonators we experimentally verify the existence of vortices in the Poynting vector describing the energy transport in a rectangular billiard. We show that these vortices appear as a consequence of the nontrivial topological structure of the underlying phase of the electromagnetic field. The results are relevant also for vortices appearing during the quantum transport.

### One-dimensional scattering systems

There is a close correspondence between one-dimensional tight-binding systems, and the propagation of microwaves through a single-mode wave guide with inserted scatterers. Varying the lengths of the scatterers arbitrary sequences of site potentials can be realized. Exemplary results on the transmission through regular and random arrangements of scatterers as well as through sequences with correlated disorder were studied.

### Field distributions in three dimensional billiards

For about 200 eigenfrequencies of a Sinai-shaped three-dimensional microwave resonator electromagnetic field distributions were mapped by measuring the eigenfrequency shift Δν as a function of the position of a spherical perturbing bead. Both regular and chaotic field patterns were found. For the chaotic field distributions all components of the electromagnetic field were found to be uncorrelated and Gaussian distributed.