Minimum action method for the Kardar-Parisi-Zhang equation

Details Minimum action method for the Kardar-Parisi-Zhang equation Minimum action method for the Kardar-Parisi-Zhang equation

2009-04-09

arxiv.org/abs/0904.1521v1

Physics

Condensed Matter

Statistical Mechanics

26 pages (revtex) and 18 figures (eps)

Scientific paper

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for a growing interface. In one dimension we find that the switching scenario is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise driven Burgers equation. The transition scenario is in accordance with recent analytical studies of the one dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit. We also briefly discuss transitions in two dimensions.

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