SANDPILES AND DIFFUSION-LIMITED REACTIONS

We establish the equivalence between a one-dimensional sandpile model recently introduced by Chhabra et al. [Phys. Rev. A (to be published)], and the diffusion-limited reaction A + A --> 0 with a point source. The equivalence is used to predict the power-law decay of the avalanche size distribution, P(s) approximately s-3, in agreement with numerical simulations. This result differs from the mean-field treatment of Chhabra et al., demonstrating the importance of fluctuations in this low-dimensional system.