  We report on an experimental investigation of the transition of a quantum
system with integrable classical dynamics to one with violated time-reversal
(T) invariance and chaotic classical counterpart. High-precision experiments
are performed with a flat superconducting microwave resonator with circular
shape in which T-invariance violation and chaoticity are induced by magnetizing
a ferrite disk placed at its center, which above the cutoff frequency of the
first transverse-electric mode acts as a random potential. We determine a
complete sequence of approx. 1000 eigenfrequencies and find good agreement with
analytical predictions for the spectral properties of the Rosenzweig-Porter
(RP) model, which interpolates between Poisson statistics expected for typical
integrable systems and Gaussian unitary ensemble statistics predicted for
chaotic systems with violated T invariance. Furthermore, we combine the RP
model and the Heidelberg approach for quantum-chaotic scattering to construct a
random-matrix model for the scattering (S) matrix of the corresponding open
quantum system and show that it perfectly reproduces the fluctuation properties
of the measured S matrix of the microwave resonator.
