Quantum Fingerprints of Classical Ruelle-Pollicott Resonances

Quantum and classical correlations are studied experimentally in model $n$-disk microwave billiards. The wave vector $\kappa$ autocorrelation $C\left(\kappa \right)$ of the quantum spectrum displays nonuniversal oscillations for large $\kappa$, comparable to the universal random matrix theory behavior observed for small $\kappa$. The nonuniversal behavior is shown to be completely determined by the classical Ruelle-Pollicott resonances, arising from the complex eigenvalues of the Perron-Frobenius operator, and calculated using periodic orbit theory. This work establishes a fundamental connection between the quantum and classical correlations of an open system.