${1/f}^{\alpha }$ noise from correlations between avalanches in self-organized criticality

We show that large, slowly driven systems can evolve to a self-organized critical state where long-range temporal correlations between bursts or avalanches produce low-frequency ${1/f}^{\alpha }$ noise. The avalanches can occur instantaneously in the external time scale of the slow drive, and their event statistics are described by power-law distributions. A specific example of this behavior is provided by numerical simulations of a deterministic “sandpile” model, where a scaling relation links $\alpha$ with the avalanche power-law exponent.