Experimental investigation of the enhancement factor and the cross-correlation function for graphs with and without time-reversal symmetry: the open system case

We present the results of an experimental study of the enhancement factor WS,β of the two-port scattering matrix S-circumflex and the cross-correlation function c12(ν) for microwave irregular networks simulating quantum graphs with time-reversal symmetry (TRS), symmetry index β=1, and without TRS, β=2, in the presence of absorption. We show that even for systems with notable losses the elastic enhancement factor WS,β remains a statistical measure that allows the determination of a symmetry class of the chaotic quantum systems under investigation. Therefore, the enhancement factor WS,β may be contrasted with many others statistical measures such as, for example, the nearest neighbor spacing distribution or the spectral rigidity, which are not directly applicable in the presence of strong absorption. The quantum graphs with TRS were simulated by the microwave networks built of coaxial cables connected by joints and attenuators, which allowed us to control absorption. The microwave circulators were added to the networks to simulate graphs with broken TRS. The experimental results are compared to the ones obtained within the framework of random matrix theory.