T. Antal et Z. Racz, DYNAMIC SCALING OF THE WIDTH DISTRIBUTION IN EDWARDS-WILKINSON TYPE MODELS OF INTERFACE DYNAMICS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(3), 1996, pp. 2256-2260
Edwards-Wilkinson type models are studied in 1+1 dimensions and the ti
me-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, usi
ng a flat interface as an initial condition, P-L(w(2),t) can be calcul
ated 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, scalin
g is observed only in the large-time limit and the scaling function de
pends on the initial amplitude of the longest wavelength mode. The sho
rt-time limit is also interesting since P-L(w(2),t) is found to closel
y 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.