The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension

Simple item page
dc.creatorFogedby, Hans C.
dc.date2005-10-11
dc.date.accessioned2026-07-07T06:44:15Z
dc.date.available2026-07-07T06:44:15Z
dc.descriptionWe extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that the growth morphology can be interpreted in terms of dynamically evolving textures of localized growth modes with superimposed diffusive modes. In the Cole-Hopf representation the growth modes are static solutions to the diffusion equation and the nonlinear Schroedinger equation, subsequently boosted to finite velocity by a Galilei transformation. We discuss the dynamics of the pattern formation and, briefly, the superimposed linear modes. Implementing the stochastic interpretation we discuss kinetic transitions and in particular the properties in the pair mode or dipole sector. We find the Hurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipole sector. Finally, applying Derrick's theorem based on constrained minimization we show that the upper critical dimension is d=4 in the sense that growth modes cease to exist above this dimension.
dc.description27 pages, 19 eps figs, revtex
dc.identifierhttps://arxiv.org/abs/cond-mat/0510268
dc.identifierhttp://arxiv.org/abs/cond-mat/0510268
dc.identifierPhys. Rev. E 73, 031104 (2006)
dc.identifierdoi:10.1103/PhysRevE.73.031104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102721
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.titleThe Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
dc.typetext

Files

Collections

arXiv