H . - J . Stöckmann

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Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a(More)
Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed conical scatterers. At high frequencies, the flow shows branching structures similar to those observed in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are responsible for these(More)
The influence of absorption on the spectra of microwave graphs has been studied experimentally. The microwave networks were made up of coaxial cables and T junctions. First, absorption was introduced by attaching a 50Ω load to an additional vertex for graphs with and without time-reversal symmetry. The resulting level-spacing distributions were compared(More)
Abstract. Using supersymmetry techniques analytical expressions for the average of the fidelity amplitude fǫ(τ) = 〈ψ(0)| exp(2πıHǫτ) exp(−2πıH0τ)|ψ(0)〉 are obtained, where the H0 and Hǫ are taken from the Gaussian unitary ensemble (GUE) or the Gaussian orthogonal ensemble (GOE), and ǫ is a parameter, characterizing the strength of a perturbation. As long as(More)
The scattering matrix was measured for a flat microwave cavity with classically chaotic dynamics. The system can be perturbed by small changes of the geometry. We define the "scattering fidelity" in terms of parametric correlation functions of scattering matrix elements. In chaotic systems and for weak coupling, the scattering fidelity approaches the(More)
From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can be considered as local since wave functions are influenced only locally, in contrast to, e.g., the situation(More)
The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the(More)
We quantify the presence of direct processes in the S matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P(S)(S) of the S matrix, i.e., S=sqrt[R]e(itheta), is studied in cavities with time-reversal symmetry for different antenna coupling strengths T(a) or direct processes. The experimental results(More)
Nodal domains are studied both for real psiR and imaginary part psiI of the wave functions of an open microwave cavity and found to show the same behavior as wave functions in closed billiards. In addition we investigate the variation of the number of nodal domains and the signed area correlation by changing the global phase phig according to(More)
We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of(More)