Quenched noise and over-active sites in sandpile dynamics

The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These sandpile models are, respectively, discretizations of the Edwards-Wilkinson equation with columnar, point-like and correlated quenched noise, with the constraint that the interface velocity is either zero or one. The constraint, embedded in the sandpile rules, gives rise to another noise component. Studies of this term for the Bak-Tang-Wiesenfeld model reveal long-range on-site correlations and that, with open boundary conditions, there is no spatial translational invariance.