Energy Level Statistics of Coupled Oscillators

We investigate the manifestation of classical chaos in the statistics of quantum energy levels of coupled oscillators. On variation of the coupling strength or energy these systems exhibit a transition from regular to fully chaotic classical motion which is reflected by a corresponding transition of quantum spectral fluctuations. Regular classical motion is associated with an uncorrelated level sequence, and chaotic motion is associated with spectral statistics of random matrix ensembles. To characterize spectral fluctuations we use the distribution of spacings between adjacent energy levels and the spectral rigidity (Δ 3 statistic). These quantities measure short and long range spectral fluctuations, respectively, and are found to respond in a different way to the underlying classical motion.