Statistics of Impedance and Scattering Matrices in Chaotic Microwave Cavities: Single Channel Case

TL;DR

This paper models the statistical properties of impedance and scattering matrices in chaotic microwave cavities with a focus on the single port case, linking random matrix theory with physical cavity features.

Contribution

It introduces a model based on chaotic eigenfunctions that reproduces universal statistical features and system-specific details of impedance and scattering matrices in chaotic cavities.

Findings

Model successfully reproduces universal features of random matrix theory.

Incorporates system-specific characteristics into statistical predictions.

Validates predictions through numerical simulations.

Abstract

We discuss a model for studying the statistical properties of the impedance ($Z$) and scattering ($S$) matrices of open electromagnetic cavities with several transmission lines or waveguides connected to the cavity. In this paper, we mainly discuss the single port case. The generalization to multiple ports is treated in a companion paper. The model is based on assumed properties of chaotic eigenfunctions for the closed system. Analysis of the model successfully reproduces features of the random matrix model believed to be universal, while at the same time incorporating features which are specific to individual systems. Statistical properties of the cavity impedance $Z$ are obtained in terms of the radiation impedance (i.e., the impedance seen at a port with the cavity walls moved to infinity). Effects of wall absorption are discussed. Theoretical predictions are tested by direct comparison with numerical solutions for a specific system. (Here the word universal is used to denote high frequency statistical properties that are shared by the members of the general class of systems whose corresponding ray trajectories are chaotic. These universal properties are, by definition, independent of system-specific details.)