Impedance and Scattering Variance Ratios of Complicated Wave Scattering Systems in the Low Loss Regime

TL;DR

This paper investigates the universal behavior of impedance variance ratios in complex wave scattering systems, confirming theoretical predictions through numerical and experimental tests in low loss regimes, including superconducting microwave cavities.

Contribution

It provides the first comprehensive numerical and experimental validation of impedance variance ratio universality in low loss wave scattering systems.

Findings

Impedance variance ratios are universal functions of system loss.

Sample size affects the observed variance ratios, especially in low loss regimes.

Experimental results with microwave cavities agree with theoretical predictions within sample limitations.

Abstract

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive formula in terms of impedance to combine the predictions of RMT and nonuniversal system-specific features. The statistics of measured wave properties generally have nonuniversal features. However, ratios of the variances of elements of the impedance matrix are predicted to be independent of such nonuniversal features and thus should be universal functions of the overall system loss. In contrast with impedance variance ratios, scattering variance ratios depends on nonuniversal features unless the system is in the high loss regime. In this paper, we present numerical tests of the predicted universal impedance variance ratios and show that an insufficient sample size can lead to apparent deviation from the theory, particularly in the low loss regime. Experimental tests are carried out in three two-port microwave cavities with varied loss parameters, including a novel experimental system with a superconducting microwave billiard, to test the variance-ratio predictions in the low loss time-reversal-invariant regime. It is found that the experimental results agree with the theoretical predictions to the extent permitted by the finite sample size.