Spectral fluctuations and 1/f noise in the order-chaos transition regime

Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In this we show that the spectrum of the system undergoing order to chaos transition displays a characteristic $f^{-\gamma}$ noise and $\gamma$ is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles respectively of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.