Asymmetric avalanche process in the theory of self-organized criticality

Exact results for an asymmetric avalanche process on a ring are obtained by the Bethe ansatz method. The mean velocity v of a particle flow is derived as a function of the topping probabilities and particle density rho. As rho increases, the system exhibits a transition from an intermittent flow to a continuous flow and the velocity v exponentially diverges at the critical point rho(c) with the index alpha = 2.