Perspectives on 1/f noise in quantum chaos

The power spectrum of the δn statistic of quantum spectra presents 1/f α noise. For chaotic systems α = 1 while for regular systems α = 2. Although the transition from regularity to chaos is non universal, for a wide variety of systems with a mixed phase space the value of α is intermediate between 1 and 2 and can be related to the fraction of regular or chaotic orbits in the total phase space. This statistic can be a very useful tool for the analysis of experimental spectra, specially in the case of missing levels or spectral sequences with mixed symmetries.