Relaxation while Settling a Scaling-Invariant Distribution of Fluctuations in Random Processes with 1/f Noise

摘要

Among the numerous steady-state random processes, those in which the power spectrum is inversely proportional to the frequency f, i.e., the so-called "1/f-"processes are of particular importance. They attract attention due to their scaling-invariant fluctuation distribution. In the general case, scaling invariance can be associated with the critical behavior or self-organization in complex systems [1]. An example of scaling-invariant behavior is the Kolmogorov turbulence when energy fluxes of various length scales arise in fluid flows, these phenomena obeying unified universal similarity laws [2]. However, not all random processes are reduced to such turbulence. Almost 80 years ago, electric-voltage fluctuations inversely proportional to the frequency were discovered in electronic devices (flicker-noise [3]). It turned out that random processes displayed by the 1/f spectrum may be encountered in a number of phenomena. In addition to the electric-current and magnetic fluctuations studied in solid-state physics, many random processes in astrophysics, geophysics, biology, and computer science also display a power spectrum inversely proportional to the frequency [4].