Avalanche correlation in power spectra

Outstanding topic on noise phenomena is the occurrence of peaks in the wide frequency range from mHz to above MHz in the power spectra of many natural systems. Recently, the challenging interest has oriented to focus the spectral peaks superimposed to the 1/f noise. Until now, all existing theories failed to explain peaked spectra. Here we highlight the role of correlation among avalanches as the main source of the noise peaks observed. The present theory is based on first principle statistics of elementary events clustered in time-amplitude correlated avalanches. A spectral power master equation suitable to explain peaked noise spectra arising from avalanche correlations is achieved analytically. Excellent agreement with our experiments in superconductors and with experiments in Escherichia coli, in single DNA molecule and in single electron tunneling is reported. Our statistical model shows that avalanche correlation gives wide peaks in the power spectrum superimposed to the 1/f behavior with high slope, a typical signature of avalanche processes.