Quantum Fingerprints of Classical Ruelle-Pollicott Resonances

Quantum and classical correlations are studied experimentally in model n-disk microwave billiards. The wave vector κ autocorrelation C(κ) of the quantum spectrum displays nonuniversal oscillations for large κ, comparable to the universal random matrix theory behavior observed for small κ. 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.