Variational Formulation for the KPZ and Related Kinetic Equations
Statistical Mechanics
2016-12-21 v1 Other Condensed Matter
Abstract
We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. The procedure used for KPZ was extended in order to derive more general forms of such a functional leading to other nonlinear kinetic equations, as well as cases with density dependent surface tension.
Keywords
Cite
@article{arxiv.0911.4800,
title = {Variational Formulation for the KPZ and Related Kinetic Equations},
author = {Horacio S. Wio},
journal= {arXiv preprint arXiv:0911.4800},
year = {2016}
}
Comments
RevTex, 8pgs, double column