Dynamic scaling of the width distribution in Edwards-Wilkinson type models of interface dynamics

Edwards-Wilkinson type models are studied in 1+1 dimensions and the time-dependent distribution P-L(w(2),t) of the square of the width of an interface w(2) is calculated for systems of size L. We find that, using a flat interface as an initial condition, P-L(w(2),t) can be calculated exactly and it obeys scaling in the form [w(2)]P-infinity(L)(w(2),t) = Phi(w(2)/[w(2)](infinity),t/L(2)), where [w(2)](infinity) is the stationary value of w(2). For more complicated initial stares, scaling is observed only in the large-time limit and the scaling function depends on the initial amplitude of the longest wavelength mode. The short-time limit is also interesting since P-L(w(2),t) is found to closely approximate the log-normal distribution. These results are confirmed by Monte Carlo simulations on a singlestep, solid-on-solid type model (roof-top model) of surface evolution.