Characterization of Fluctuations of Impedance and Scattering Matrices in Wave Chaotic Scattering

Abstract

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, $V{R}_z$ and $V{R}_s$, where $V{R}_z=Var[Z_{ij}]/\{Var[Z_{ii}]Var[Z_{jj}]{\}}^{1/2}$, $V{R}_s=Var[S_{ij}]/\{Var[S_{ii}]Var[S_{jj}]{\}}^{1/2}$, and $Var[.]$ denotes variance. $V{R}_z$ is shown to be a universal function of distributed losses within the scatterer. That is, $V{R}_z$ is independent of nonuniversal coupling details. This contrasts with $V{R}_s$ for which universality applies only in the large loss limit. Explicit results are given for $V{R}_z$ 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.

6 pages, 5 figures, updated with referees' comments

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