Product measures and dynamics for solid-on-solid interfaces

A two-species asymmetric exclusion process is considered with general transition rates subject only to the constraint of charge conservation. Conditions for the existence of a stationary product measure are found in both the cases of odd-even parallel dynamics and continuous-time dynamics. The results are then applied to a one-dimensional restricted solid-on-solid model, considered as a model of driven interfacial growth, showing a nontrivial dependence of the stationary measure on the external driving field. The dependence of the growth velocity on the slope of the interface is given and interface shapes in finite volume with opposite boundary conditions are investigated numerically