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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 supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.

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 linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely imaginary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.

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 fidelity of the closed system. Without free parameters, the experimental results agree with random matrix theory in a wide range of perturbation strengths, reaching from the perturbative to the Fermi golden rule regime.

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 are compared with random-matrix calculations and with numerical simulations including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with theoretical predictions for all cases.

We investigate the statistical properties of wave functions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wave functions cross over from real to complex. The distribution of the phase rigidity, which characterizes the degree to which a wave function is complex, and long-range correlations of intensity and current density are studied as a function of the number of channels in the openings. All measured quantities are in perfect agreement with theoretical predictions.

We measure the transmission through asymmetric and reflection-symmetric chaotic microwave cavities in dependence on the number of attached waveguides. Ferrite cylinders are placed inside the cavities to break time-reversal symmetry. The phase-breaking properties of the ferrite and its range of applicability are discussed in detail. We use the random matrix theory accounting for absorption effects to calculate the universal distribution of transmission coefficients T and their energy derivatives dT/depsilon. Using the absorption strength as a fitting parameter, we find good agreement between universal transmission fluctuations predicted by the theory and the experimental data.