In a sequence of two talks microwave experiments on spectra, line widths, and field distributions in various closed and open microwave resonators are presented with special emphasis on universal features common to all chaotic systems.
According to a conjecture of Berry (1977) at any point in a chaotic billiard
the wave function may be described by a random superposition of plane waves,
In this lecture microwave experiments are presented, exploiting further consequences of the Berry conjecture. Results for field distributions and spatial correlation functions in three-dimensional Sinai resonators (Dörr et al 1998) are presented. For spectral level dynamics in a disordered system with the position of one impurity as the parameter the approach allows to calculate velocity distributions and velocity autocorrelation functions which are in complete agreement with the experiment (Barth et al 1999). In open billiards and billiards with broken time-reversal symmetry the distributions of currents and vortices, as well as the vortex distance distribution are measured and compared with the prediction from the Berry conjecture (Barth and Stöckmann, Vranicar et al).
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Dörr U, Stöckmann H J, Barth M and Kuhl U 1998 Phys. Rev. Lett. 80 1030
Barth M, Kuhl U and Stöckmann H J 1999 Phys. Rev. Lett. 82 2026
Barth M and Stöckmann H J Current and vortex statistics in microwave billiards, to be published
Vranicar M et al. `Persistent currents' and eigenfunctions in microwave resonators with broken time reversal symmetry, to be published
Whenever a microwave experiment is performed, the system has to be opened either by attaching wave guides or introducing antennas. This has the unavoidable consequence that the system is perturbed, and the measurement always yields an unwanted combination of properties of the system and the apparatus. A tailor-made approach to cope with this situation is provided by scattering theory. For the case of isolated resonances an expression for the matrix elements of the scattering matrix is obtained,
This correspondence of microwave billiards with atomic nuclei can be used to check predictions from theory which are unaccessible in nuclear physics. As an example the first unambiguous demonstration of resonance trapping is presented, namely the phenomenon that with increasing coupling strength the widths of the resonances do not increase unlimited but finally decrease again (Persson et al 2000). If the transmission through a cavity with a number of incoming and outgoing channels is measured as a function of frequency, irregular fluctuations are observed, an equivalent to the Ericson fluctuations observed in nuclear scattering processes. The distribution of these fluctuations was studied in an open microwave billiard in dependence of the number of channels, both for systems with and without time-reversal symmetry, and the results were compared with random matrix predictions (Schanze et al 2001). A new parameter comes into play if absorption is involved, which is unavoidable in experiments anyway, but has been considered by theory only recently (Beenakker and Brouwer 2001). Again the experiment is able to verify the theoretical predictions perfectly (Méndez et al).
Stein J, Stöckmann H J and Stoffregen U Phys. Rev. Lett. 75 53
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Persson E, Rotter I, Stöckmann H J and Barth M 2000 Phys. Rev. Lett. 85 2478
Schanze H, Alves E, Lewenkopf C and Stöckmann H J 2001 Phys. Rev. E 64 065201(R)
Beenakker C and Brouwer P 2001 Physica E 9 463
Méndez-Sánchez R et al. Distribution of reflection eigenvalues in absorbing chaotic microwave cavities, to be published