Power spectrum of the current in systems with a conserved density

Motivated by recent studies of model sandpiles, the power spectrum S of the current in dissipative dynamical systems with a conserved density is investigated. In contrast to self-organized criticality exhibited in certain lattice gases and noisy Langevin equations, where power laws are described by universal, simple indices, the index of S(f) for small frequency f is determined at a second-order phase transition by nontrivial critical exponents. For systems with no external drive (i.e., model B), the exact result for the dynamic exponent z is rederived. With drive (driven diffusive systems), the index is given by the exponent of anisotropies. Simulation in two dimensions yields good agreements with theoretical predictions.