  We show that the autocorrelation of quantum spectra of an open chaotic system
is well described by the classical Ruelle-Pollicott resonances of the
associated chaotic strange repeller. This correspondence is demonstrated
utilizing microwave experiments on 2-D n-disk billiard geometries, by
determination of the wave-vector autocorrelation C(\kappa) from the
experimental quantum spectra S_{21}(k). The correspondence is also established
via "numerical experiments" that simulate S_{21}(k) and C(\kappa) using
periodic orbit calculations of the quantum and classical resonances.
Semiclassical arguments that relate quantum and classical correlation functions
in terms of fluctuations of the density of states and correlations of particle
density are also examined and support the experimental results. The results
establish a correspondence between quantum spectral correlations and classical
decay modes in an open systems.
