Experimental investigation of universal parametric correlators using a vibrating plate

TL;DR

This study experimentally investigates how eigenfrequencies of a chaotic vibrating plate vary with external parameters, confirming the applicability of random matrix theory's universal correlation functions to classical wave systems.

Contribution

It demonstrates the experimental validation of universal parametric correlators in a classical chaotic system, extending random matrix theory's relevance beyond quantum systems.

Findings

Eigenfrequency correlations match random matrix theory predictions

Sensitivity to pressure isolates specific symmetry class modes

Eigenvalues exhibit oscillations consistent with theoretical models

Abstract

The parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions. The sensitivity of the flexural modes of the plate to pressure is used to isolate this symmetry class of modes and simplify the data analysis. The size of the plate is used as the external parameter and the eigenvalues are observed to undergo one or two oscillations in the experimental window. The correlations of the eigenvalues are in good agreement with statistical measures such as the parametric number variance, the velocity autocorrelation, and the intralevel velocity autocorrelation derived for the Gaussian Orthogonal Ensemble of random matrix theory. Our results show that the theory can be also applied to wave systems other than quantum systems.