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We report on the experimental investigation of the properties of theeigenvalues and wavefunctions and the fluctuation properties of the scatteringmatrix of closed and open billiards, respectively, of which the classicaldynamics undergoes a transition from integrable via almost integrable to fullychaotic. To realize such a system we chose a billiard with a 60 degree sectorshape of which the classical dynamics is integrable, and introduced circularscatterers of varying number, size and position. The spectral properties ofgeneric quantum systems of which the classical counterpart is either integrableor chaotic are universal and well understood. If, however, the classicaldynamics is pseudo-integrable or almost-integrable, they exhibit anon-universal intermediate statistics, for which analytical results are knownonly in a few cases, like, e.g., if it corresponds to semi-Poisson statistics.Since the latter is, above all, clearly distinguishable from those ofintegrable and chaotic systems our aim was to design a billiard with thesefeatures which indeed is achievable by adding just one scatterer of appropriatesize and position to the sector billiard. We demonstrate that, while thespectral properties of almost-integrable billiards are sensitive to theclassical dynamics, this is not the case for the distribution of thewavefunction components, which was analysed in terms of the strengthdistribution, and the fluctuation properties of the scattering matrix whichcoincide with those of typical, fully chaotic systems.

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards