Experimental tests of random wave models with chaotic microwave billiards
In this work we shall test predictions of random wave models with microwave experiments. In wave or quantum mechanical systems, where the classical dynamic is chaotic, we can make predictions on quantities which only depend on general properties of the wave function. In our experiments on quasi two-...
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|Zusammenfassung:||In this work we shall test predictions of random wave models with microwave experiments. In wave or quantum mechanical systems, where the classical dynamic is chaotic, we can make predictions on quantities which only depend on general properties of the wave function. In our experiments on quasi two-dimensional microwave cavities we use the complete equivalence of the Schrödinger equation and the Helmholtz equation to study properties of quantum systems with electromagnetical waves. In the first part of this thesis we investigate spatial correlation functions of open billiard systems. In open quantum systems we expect running waves as the solution of the Schrödinger equation. Thus the wave function is complex and the zeros of a two-dimensional complex function are nodal points and not nodal lines as we would expect for a closed system. In this work we shall investigate the spatial correlation function between nodal points of the wave function and saddle points of the phase of the wave function. For this correlation function we will additionally look for the influence of the boundary due to the finite size of the system. Another quantity one can study is the distribution of the components of the quantum stress tensor. In the second part we shall study the time dependent stability of a quantum system against a local perturbation. The time dependent stability of a quantum system is described by the fidelity, which is defined as the overlap integral of the time evolution of the same initial state under an unperturbed and a perturbed Hamiltonian. Experimentally the local perturbation has been realized by the shift of a small scatterer. We use the model of random plane waves to calculate a theoretical expression for the fidelity of a local perturbation and compare this to our experimental results. In the last part of this work we shall present an analogue experiment with microwaves to investigate the probability of extreme wave heights in the ocean. Such high amplitudes in the ocean are called freak waves, rogue waves or sometimes giant waves. Data of wave heights collected with radar satellite suggests that a random wave model surely underestimates the probability of such events. One way to explain the higher probability for freak waves is the effect of focussing of waves due to variable velocity fields. These velocity fields can be formed by current eddies or a height variation in shallow water. In our analogue study we use a potential landscape for microwaves to show the influence of focussing effects on the distribution of intensities.|