Chaos and 1/f noise in quantum systems

The energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum of such signal gives rise to 1/f noise in chaotic systems, whereas integrable systems present 1/f 2 noise. This statistic is very useful for the analysis of two kinds of imperfect spectra: those with missing levels whose number and position are unknown, and those in which all the quantum numbers cannot be determined and levels of different symmetries are mixed. The power spectrum analysis provides an estimation of the number of symmetries and the fraction of mixing and missing levels.