  N-disk microwave billiards, which are representative of open quantum systems,
are studied experimentally. The transmission spectrum yields the quantum
resonances which are consistent with semiclassical calculations. The spectral
autocorrelation of the quantum spectrum is shown to be determined by the
classical Ruelle-Pollicot resonances, arising from the complex eigenvalues of
the Perron-Frobenius operator. This work establishes a fundamental connection
between quantum and classical correlations in open systems.
