Patterns in the Kardar-Parisi-Zhang equation

Abstract

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence of an upper critical dimension.

8 pages revtex, 4 eps figures

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• Dynamical Inequality in Growth Models
• Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
• Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation
• Stirred Kardar-Parisi-Zhang equation with quenched random noise: Emergence of induced nonlinearity
• The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime