We study a system of hard-core particles sliding locally downwards on a fluctuating one-dimensional surface characterized by a dynamical exponent $z$ and no overall tilt. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale $\sim t^{1/z}$. The structure factor deviates from the Porod law for the models studied. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provide insight into this behavior.

• Received 18 February 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.1602