Universal scaling function and amplitude ratios in surface growth

A scaling analysis of the Kardar-Parisi-Zhang equation for driven interface growth, as a function of the hydrodynamical parameters λ, D, and ν, is presented in d=2, which predicts the existence of universal amplitude ratios as well as a universal scaling function for the surface width w(L,t) on length scales L at time t. These predictions are confirmed by simulations of three different models as well as a mode-coupling calculation with which good agreement is found. This scaling analysis is expected to be useful in establishing a more detailed connection between continuum equations, microscopic models, and experiments.