Quantum Correlations and Classical Resonances in an Open Chaotic System

Abstract

We show that the autocorrelation of quantum spectra of an open chaotic system is well described by the classical RuellePollicott 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(κ) from the experimental quantum spectra S21(k). The correspondence is also established via "numerical experiments" that simulate S21(k) and C(κ) 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.