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

TL;DR

This paper investigates the universal and nonuniversal fluctuations of impedance and scattering matrices in wave chaotic systems, revealing that impedance variance ratios are universal functions of internal losses, supported by experimental data.

Contribution

It introduces the impedance and scattering variance ratios, showing impedance ratios are universal functions of internal losses, unlike scattering ratios which depend on coupling details.

Findings

$VR_z$ is a universal function of internal losses.

$VR_s$ is only universal in the high-loss limit.

Experimental data confirms the theoretical predictions.

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