From ballistic deposition to the Kardar-Parisi-Zhang equation through a limiting procedure

Takashi Nagatani

Type: Article

Publication Date: 1998-07-01

Citations: 22

DOI: https://doi.org/10.1103/physreve.58.700

Abstract

We show a direct connection between the ballistic deposition and the Kardar-Parisi-Zhang (KPZ) equation. We derive the KPZ equation from the ballistic deposition models, using an important limiting procedure. The cellular automaton rule is transformed into an integrable difference-difference equation through the limiting procedure. By applying the perturbation method to the difference-difference equation, the difference-difference equation is reduced to the KPZ equation through the Burgers equation. We apply the procedure to several types of ballistic deposition models.

Locations

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics - View
Shizuoka University Repository (Shizuoka University) - View - PDF

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+ PDF Chat	Fluctuations of a stationary nonequilibrium interface	1991	Bernard Derrida Joel L. Lebowitz Eugène R. Speer Herbert Spohn
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