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 well-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 time scale imposed by the external deposition and study the autocorrelation 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 correlations become stronger in the limit of large system size. We independently test this result by calculating the power spectrum of the series of successive avalanche lifetimes and sizes. For large system sizes L there is a frequency regime where the power spectrum tends to a 1/f type of noise, in agreement with the tendency of the autocorrelation function to approach a constant in large systems.