Studies of chaotic Dynamics in a Three-Dimensional Superconducting Microwave Billiard

We present first measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped like a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally derived for quantum systems like eigenvalue statistics and periodic orbits and obtain according to a model of Berry and Robnik a mixing parameter of about 25%. In numerical simulations of the classical motion in the cup the degree of chaoticity has been estimated. This leads to an invariant chaotic Liouville measure of about 45%. The difference between this figure and the mixing parameter is due to the limited accuracy of the statistical analysis, caused by both, the fairly small number of 286 resonances and the rather poor desymmetrization of the microwave cavity. Concerning the periodic orbits of the classical system we present a comparison with the length spectrum of the resonator and introduce a new bouncing ball formula for electromagnetic billiards.Comment: 9 pages (RevTex) , 10 figures included, full resolution figures are available upon request from [email protected], to be published in Phys. Rev.

Remembering the bad old days: Human rights, economic conditions, and democratic performance in transitional regimes

Using the natural laboratory of 18 post-communist Central and Eastern European countries, this article presents a basic model for democratic transition, specifically testing two alternative explanations for the degree of citizen satisfaction with the performance of their fledgling democracies: 1) virtues of omission, which include bad actions from which the state refrains, namely violations of individual human rights, and 2) virtues of commission, which include positive state actions, in particular actions enhancing economic well-being. The findings clearly indicate that, during the transition period, citizens' sense of the condition of human rights is consistently more important than are perceived economic prospects as predictors of democratic performance. -- In der Untersuchung werden zwei alternative Hypothesen getestet, die den Grad der Zufriedenheit der Bürger mit der Performanz der Demokratie in 18 post-kommunistischen Ländern erklären sollen. Die eine Hypothese betont die Wichtigkeit der Garantie der individuellen Menschenrechte, die andere die Wichtigkeit der Verbesserung der ökonomischen Situation. In dem einen Fall soll sich der Staat menschenrechtsverletzender Handlungen enthalten (virtues of ommission), in dem anderen Fall soll er zur Hebung des wirtschaftlichen Wohlstands politisch eingreifen (virtues of commission). Der Befund zeigt, daß in der Übergangsperiode vom post-kommunistischen zum demokratischen Regime den Bürgern der Zustand der Menschenrechte für das Urteil über die Leistungsfähigkeit der Demokratie im eigenen Lande relativ wichtiger ist als die wirtschaftliche Entwicklung.

Democracy and its discontents in post-wall Germany

This paper traces the political behavior intentions of satisfied democrats, dissatisfied democrats, and non-democrats in western and eastern Germany. Dissatisfaction is most commonly expressed in support for the loyal opposition, with some minor tilt toward parties of the ends of the spectrum. Non-democrats, a very small percentage of the populace, more commonly express their disapproval through withdrawal rather than through active extremism. Based on a 1997 general population survey, the analysis reveals some differences in the magnitude of western versus eastern conceptions of the elements that make up democracy. But most of those differences get channeled into seemingly benign forms of political participation. The core of the findings is that dissatisfaction with democracy may well be a healthy stimulant rather than a threat to the vitality of either established or emerging democracies. -- Die hier vorgelegte Untersuchung analysiert politische Einstellungen und Verhaltensabsichten von zufriedenen Demokraten, unzufriedenen Demokraten und Nicht-Demokraten in Ost- und Westdeutschland. Unzufriedenheit mit der Politik führt in der Regel zu einer verstärkten Unterstützung demokratischer Oppositionsparteien, unter bestimmten Bedingungen aber auch zur Wahl extremer Oppositionsparteien. Die Untersuchung ergibt, dass Nicht-Demokraten, die in Ost- und Westdeutschland allerdings nur einen sehr geringen Prozentsatz ausmachen, ihre Unzufriedenheit weniger durch die Wahl einer extremen Partei, als durch einen Rückzug aus der Politik ausdrücken. Die Daten der repräsentativen Bevölkerungsumfrage zeigen in einigen Aspekten Unterschiede in bestimmten Wertorientierungen und im Demokratieverständnis der Ost- und der Westdeutschen. Daraus ergeben sich allerdings keine gravierenden Konsequenzen für den demokratischen Prozess. In beiden Teilen Deutschlands führen politische Unzufriedenheiten in aller Regel zur Wahl demokratischer Oppositionsparteien. Unzufriedenheit mit der Performanz des demokratischen Systems in Deutschland kann deshalb eher als Stimulus und weniger als Bedrohung der Demokratie interpretiert werden.

Correlation-Hole Method for Spectra of Superconducting Microwave Billiards

The spectral fluctuation properties of various two- and three-dimensional superconducting billiard systems are investigated by employing the correlation-hole method. It rests on the sensitivity of the spectral Fourier transform to long range correlations and is thus an alternative technique to study chaotic dynamics. First, we apply the method to the eigenfrequencies which are extracted from the measured resonances. Second, we analyze the unfolded raw spectra, including the shape of the resonances. The merit of the method lies in a clear separation of the statistics due to the positions and due to the shape of the resonances. However, we show that statistical fluctuations of the intensities of the resonances have a strong impact on the observable. Therefore, the visibility of the correlation hole is studied as a function of the number of independent statistical variables entering into the intensities. The visibility improves if independent spectra are superimposed.Comment: 12 pages (Latex) including 10 postscript figures; to be published in Phys. Rev. E; Info: [email protected]

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]

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.

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.

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]

Coupled Microwave Billiards as a Model for Symmetry Breaking

Two superconducting microwave billiards have been electromagnetically coupled in a variable way. The spectrum of the entire system has been measured and the spectral statistics analyzed as a function of the coupling strength. It is shown that the results can be understood in terms of a random matrix model of quantum mechanical symmetry breaking -- as e.g. the violation of parity or isospin in nuclear physics.Comment: 4 pages, 5 figure

Pathfinder first light: alignment, calibration, and commissioning of the LINC-NIRVANA ground-layer adaptive optics subsystem

We present descriptions of the alignment and calibration tests of the Pathfinder, which achieved first light during our 2013 commissioning campaign at the LBT. The full LINC-NIRVANA instrument is a Fizeau interferometric imager with fringe tracking and 2-layer natural guide star multi-conjugate adaptive optics (MCAO) systems on each eye of the LBT. The MCAO correction for each side is achieved using a ground layer wavefront sensor that drives the LBT adaptive secondary mirror and a mid-high layer wavefront sensor that drives a Xinetics 349 actuator DM conjugated to an altitude of 7.1 km. When the LINC-NIRVANA MCAO system is commissioned, it will be one of only two such systems on an 8-meter telescope and the only such system in the northern hemisphere. In order to mitigate risk, we take a modular approach to commissioning by decoupling and testing the LINC-NIRVANA subsystems individually. The Pathfinder is the ground-layer wavefront sensor for the DX eye of the LBT. It uses 12 pyramid wavefront sensors to optically co-add light from natural guide stars in order to make four pupil images that sense ground layer turbulence. Pathfinder is now the first LINC-NIRVANA subsystem to be fully integrated with the telescope and commissioned on sky. Our 2013 commissioning campaign consisted of 7 runs at the LBT with the tasks of assembly, integration and communication with the LBT telescope control system, alignment to the telescope optical axis, off-sky closed loop AO calibration, and finally closed loop on-sky AO. We present the programmatics of this campaign, along with the novel designs of our alignment scheme and our off-sky calibration test, which lead to the Pathfinder's first on-sky closed loop images