Excess Noise for Driven Diffusive Systems

We investigate the steady-state scattering function for driven diffusive systems with a single conserved density. In one dimension, density fluctuations spread as $t^{\frac{2}{3}}$, i.e., faster than the diffusive $t^{\frac{1}{2}}$, for large time $t$. The corresponding excess noise in the current-current correlation diverges as ${\omega }^{-\frac{1}{3}}$ for small frequency $\omega$. Monte Carlo simulation results for a driven hard-core lattice gas confirm these results. $d=2\mathrm{}$ is the borderline dimension with marginally nondiffusive behavior; for $d>\mathrm{}2\mathrm{}$, the spread is diffusive with anisotropic long-time-tail corrections.