Characterization of fluctuations of impedance and scattering matrices in wave chaotic scattering

In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, Ξz and Ξₛ, where Ξz=Var[Zᵢⱼ]∕Var[Zᵢᵢ]Var[Zⱼⱼ]1∕2, Ξₛ=Var[Sᵢⱼ]∕Var[Sᵢᵢ]Var[Sⱼⱼ]1∕2, and Var[∙] denotes variance. Ξz is shown to be a universal function of distributed losses within the scatterer. That is, Ξz is independent of nonuniversal coupling details. This contrasts with Ξₛ for which universality applies only in the large loss limit. Explicit results are given for Ξz for time reversal symmetric and broken time reversal symmetric systems. Experimental tests of the theory are presented using data taken from scattering measurements on a chaotic microwave cavity.