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

Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics