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Microwave Measurements on n-Disk Systems and Investigation of Branching in correlated Potentials and turbulent Flows
In this work we investigate the wave propagation in three different complex systems. In the first two systems we focus on the wave propagation through random potentials, the first one in a microwave and the second one in an acoustic setup. In both systems we focus on the non-Gaussian properties of t...
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| Format: | Dissertation |
| Sprache: | Englisch |
| Veröffentlicht: |
Philipps-Universität Marburg
2013
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| Zusammenfassung: | In this work we investigate the wave propagation in three different complex systems. In the first two systems we focus on the wave propagation through random potentials, the first one in a microwave and the second one in an acoustic setup. In both systems we focus on the non-Gaussian properties of the measured quantities. The third system is a paradigmatic example of a fully chaotic open system with a fractal repeller. Here the relation of the classical periodic orbits and quantum mechanical quantities is studied.
In the first experiment we induce a potential into the microwave cavity by placing randomly distributed metallic scatterers on the bottom plate. Spatially resolved measurements of the full wave function reveal strong intensity fluctuations and a condensation of the wave flow along classical caustics. Additionally the scaling behavior of the branching with respect to the standard deviation of the potential is investigated and the predicted exponent of $-2/3$ is reproduced. As there are several open modes in the cavity due to the high frequency, effects of mode interference and mode coupling are found and explained, which go beyond the theoretical model. Perturbation theory of the Helmholtz equation for non-parallel top and bottom plate reveals extra source terms for the wave function, which are induced by the other open modes. These dynamics are also found in the experimental data.
The second experiment deals with an acoustic setup, where the sound of a turbulent air flow is recorded. Here strong deviations from the central limit theorem, which predicts a Gaussian distribution of wave intensities, are observed. In a second experiment performed in a wind tunnel a monochromatic sound wave is sent through the air flow. The hope to learn something about the properties of the turbulence by investigating the modulations of the original sound is not met. But again non-Gaussian behavior is found.
In the third part of this thesis another complex system is studied in a microwave setup: The emph{n}-disk system consists of emph{n} equal disks placed on an equilateral polygon in a two dimensional plane. Such an open systems provides complex resonances, which are extracted from our measured spectra via an elaborate algorithm, the harmonic inversion. The challenges of this extraction are discussed in detail and possible solutions for arising problems are suggested. The finally obtained resonances are used for the calculation of the counting function of the real parts, whose growth is predicted by the Hausdorff dimension as leading order. The distributions of the imaginary parts are studied with respect to the opening of the system. The largest (negative) imaginary part defines the spectral gap, which is compared to predictions, which can be calculated by using the periodic orbits of the system. By similar means a suggestions for the development of the maximum of this distribution is tested. Moreover the experimental data is compared to the quantum mechanical calculation of the system. |
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| DOI: | 10.17192/z2013.0457 |