Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems

TL;DR

This study experimentally investigates the universal statistical properties of the eigenvalues of scattering, impedance, and admittance matrices in wave-chaotic systems, demonstrating their dependence on loss and confirming predictions from Random Matrix Theory.

Contribution

It introduces a matrix-normalization method to remove direct processes and validates RMT predictions for eigenvalue distributions in wave-chaotic systems.

Findings

Eigenvalue PDFs match RMT predictions

Eigenphase joint PDFs evolve with loss as theory suggests

Normalization effectively isolates universal properties

Abstract

Statistical fluctuations in the eigenvalues of the scattering, impedance and admittance matrices of 2-Port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity. We remove the direct processes introduced by the non-ideally coupled driving ports through a matrix-normalization process that involves the radiation-impedance matrix of the two driving ports. We find good agreement between the experimentally obtained marginal probability density functions (PDFs) of the eigenvalues of the normalized impedance, admittance and scattering matrix and those from Random Matrix Theory (RMT). We also experimentally study the evolution of the joint PDF of the eigenphases of the normalized scattering matrix as a function of loss. Experimental agreement with the theory by Brouwer and Beenakker for the joint PDF of the magnitude of the eigenvalues of the normalized scattering matrix is also shown.