Spectral statistics in an open parametric billiard system

We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal ensembles of random matrices are found. They are explained by treating the billiard as an open scattering system in which microwave power is coupled in and out via antennas. To study the interaction of the quantum (or wave) system with its environment, a highly sensitive parametric correlator is used.

Figure 1

Sketch of the billiard, showing the outer boundary, as well as the rotatable wedge-shaped piece of teflon. The angle of rotation $\alpha$ of the wedge defines the parameter (its initial orientation is arbitrary).

Figure 2

Part (#200–#250) of the experimental eigenvalues on an unfolded (i.e., dimensionless) scale as a function of the parameter $\alpha$.

Figure 3

The experimental nearest-neighbor spacing distribution (histogram); the GOE random matrix result (full line). The eigenvalues #331 to #440 of each of the 37 spectra have been used.

Figure 4

The experimental distribution of avoided crossings (full line histogram) compared to the GOE prediction Eq. (2) (full line curve). The dashed line histogram is obtained from the model (4) with $\lambda =0.02$ and using a discrete set of rescaled parameters ${\mu }_{\mathit{resc}}$ (see main text). The eigenvalues #331 to #440 of each of the 37 spectra have been used.