TEMPORAL CORRELATIONS IN A ONE-DIMENSIONAL SANDPILE MODEL

We investigate numerically temporal correlations in a one-dimensional critical-slope sandpile model with rules that on average conserve the number of particles. Our work is motivated by the existence of two wel l-separated time scales in self-organized sandpile models, one related to the spreading of avalanches and the other imposed by the external driving. We assume that avalanches are instantaneous events on the tim e scale imposed by the external deposition and study the autocorrelati on function of the series of successive avalanche amplitudes. We find that the autocorrelation function has a log-normal form and for large system sizes tends to a constant, implying that the temporal correlati ons become stronger in the limit of large system size. We independentl y test this result by calculating the power spectrum of the series of successive avalanche lifetimes and sizes. For large system sizes L the re is a frequency regime where the power spectrum tends to a 1/f type of noise, in agreement with the tendency of the autocorrelation functi on to approach a constant in large systems.