Criticality and long-range correlations in time series in classical and quantum systems

We present arguments which indicate that a transitional state in between two different regimes implies the occurrence of 1/f time series and that this property is generic in both classical and quantum systems. Our study focuses on two particular examples: the one-dimensional module-1 logistic map and nuclear excitation spectra obtained with a schematic shell-model Hamiltonian. We suggest that a transitional point is characterized by the long-range correlations implied by 1/f time series. We apply a Fourier spectral analysis and the detrended fluctuation analysis method to study the fluctuations to each system.