R-matrix theory of driven electromagnetic cavities

Resonances of cylindrical symmetric microwave cavities are analyzed in R-matrix theory which transforms the input channel conditions to the output channels. Single and interfering double resonances are studied and compared with experimental results, obtained with superconducting microwave cavities. Because of the equivalence of the two-dimensional Helmholtz and the stationary Schroedinger equations, the results present insight into the resonance structure of regular and chaotic quantum billiards.Comment: Revtex 4.

Experimental vs. Numerical Eigenvalues of a Bunimovich Stadium Billiard -- A Comparison

We compare the statistical properties of eigenvalue sequences for a gamma=1 Bunimovich stadium billiard. The eigenvalues have been obtained by two ways: one set results from a measurement of the eigenfrequencies of a superconducting microwave resonator (real system) and the other set is calculated numerically (ideal system). The influence of the mechanical imperfections of the real system in the analysis of the spectral fluctuations and in the length spectra compared to the exact data of the ideal system are shown. We also discuss the influence of a family of marginally stable orbits, the bouncing ball orbits, in two microwave stadium billiards with different geometrical dimensions.Comment: RevTex, 8 pages, 8 figures (postscript), to be published in Phys. Rev.

Anderson Localization in a String of Microwave Cavities

The field distributions and eigenfrequencies of a microwave resonator which is composed of 20 identical cells have been measured. With external screws the periodicity of the cavity can be perturbed arbitrarily. If the perturbation is increased a transition from extended to localized field distributions is observed. For very large perturbations the field distributions show signatures of Anderson localization, while for smaller perturbations the field distribution is extended or weakly localized. The localization length of a strongly localized field distribution can be varied by adjusting the penetration depth of the screws. Shifts in the frequency spectrum of the resonator provide further evidence for Anderson localization.Comment: 7 pages RevTex, to be published in Phys. Rev.

Mode Fluctuation Distribution for Spectra of Superconducting Microwave Billiards

High resolution eigenvalue spectra of several two- and three-dimensional superconducting microwave cavities have been measured in the frequency range below 20 GHz and analyzed using a statistical measure which is given by the distribution of the normalized mode fluctuations. For chaotic systems the limit distribution is conjectured to show a universal Gaussian, whereas integrable systems should exhibit a non-Gaussian limit distribution. For the investigated Bunimovich stadium and the 3D-Sinai billiard we find that the distribution is in good agreement with this prediction. We study members of the family of limacon billiards, having mixed dynamics. It turns out that in this case the number of approximately 1000 eigenvalues for each billiard does not allow to observe significant deviations from a Gaussian, whereas an also measured circular billiard with regular dynamics shows the expected difference from a Gaussian.Comment: 7 pages, RevTex, 5 postscript figure, to be published in Phys. Rev. E. In case of any problems contact A. Baecker ([email protected]) or H. Rehfeld ([email protected]

Wave Dynamical Chaos in a Superconducting Three-Dimensional Sinai Billiard

Based on very accurate measurements performed on a superconducting microwave resonator shaped like a desymmetrized three-dimensional (3D) Sinai billiard, we investigate for the first time spectral properties of the vectorial Helmholtz, i.e. non-quantum wave equation for a classically totally chaotic and theoretically precisely studied system. We are thereby able to generalize some aspects of quantum chaos and present some results which are consequences of the polarization features of the electromagnetic waves.Comment: 4 pages RevTex; 4 postscript figures; to be published in Phys. Rev. Lett.; Info: [email protected]

Experimental Test of a Trace Formula for a Chaotic Three Dimensional Microwave Cavity

We have measured resonance spectra in a superconducting microwave cavity with the shape of a three-dimensional generalized Bunimovich stadium billiard and analyzed their spectral fluctuation properties. The experimental length spectrum exhibits contributions from periodic orbits of non-generic modes and from unstable periodic orbit of the underlying classical system. It is well reproduced by our theoretical calculations based on the trace formula derived by Balian and Duplantier for chaotic electromagnetic cavities.Comment: 4 pages, 5 figures (reduced quality

Phase shift experiments identifying Kramers doublets in a chaotic superconducting microwave billiard of threefold symmetry

The spectral properties of a two-dimensional microwave billiard showing threefold symmetry have been studied with a new experimental technique. This method is based on the behavior of the eigenmodes under variation of a phase shift between two input channels, which strongly depends on the symmetries of the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been identified by a simple and purely experimental method. This set clearly shows Gaussian unitary ensemble statistics, although the system is time-reversal invariant.Comment: RevTex 4, 5 figure

Resonance scattering and singularities of the scattering function

Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel.Comment: 4 pages, 3 figure

Crossing of two Coulomb-Blockade Resonances

We investigate theoretically the transport of non--interacting electrons through an Aharanov--Bohm (AB) interferometer with two quantum dots (QD) embedded into its arms. In the Coulomb-blockade regime, transport through each QD proceeds via a single resonance. The resonances are coupled through the arms of the AB device but may also be coupled directly. In the framework of the Landauer--Buttiker approach, we present expressions for the scattering matrix which depend explicitly on the energies of the two resonances and on the AB phase. We pay particular attention to the crossing of the two resonances.Comment: 15 pages, 1 figur