1/f noise at long time scales in self-organized criticality

We show that slowly driven systems may evolve to a self-organized critical state where correlations between avalanche events produce $1/f^{\alpha}$ noise at long time scales. The avalanche sizes are distributed according to a power law, $P(s) \sim s^{-\tau}$, and happen instantaneously in the limit of slow driving. This is confirmed by numerical simulations of a simple deterministic ``train'' model, where the exponents at the slow external time scale, e.g. $\alpha=(5\tau - 7)/(\tau-1)\simeq 1.38$, are determined only by the critical coefficient of the avalanche distribution, $\tau$.