Improved discretization of the Kardar-Parisi-Zhang equation

Chi-Hang Lam, F. G. Shin
1998 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We propose a spatial discretization of the Kardar-Parisi-Zhang ͑KPZ͒ equation in 1ϩ1 dimensions. The exact steady state probability distribution of the resulting discrete surfaces is explained. The effective diffusion coefficient, nonlinearity, and noise strength can be extracted from three correlators, and are shown to agree exactly with the nominal values used in the discrete equations. Implications on the conventional method for direct numerical integration of the KPZ equation are discussed.
doi:10.1103/physreve.58.5592 fatcat:ha437l464bhu5hbufuvh5mzacy