Generalized discretization of the Kardar-Parisi-Zhang equation

Details Generalized discretization of the Kardar-Parisi-Zhang equation Generalized discretization of the Kardar-Parisi-Zhang equation

2004-10-20

arxiv.org/abs/cond-mat/0410515v1

Physics

Condensed Matter

Other Condensed Matter

9 pages

Scientific paper

10.1103/PhysRevE.72.017701

We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any discretization scheme. We show that the discretization prescription is a consequence of each particular model. From the ballistic deposition model we derive the discretization prescription of the corresponding KPZ equation.

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