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Variational Formulation for the KPZ Equation: Consistency, Galilean-invariance violation, and fluctuation-dissipation issues in real-space discretization

AuthorsWio, Horacio S. ; Revelli, Jorge A.; Deza, R. R.; Escudero, Carlos; Lama, M. S. de la
Issue DateDec-2009
Citation12th International Workshop on Instabilities and Non-Equilibrium Structures (2009)
AbstractWe 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 [1]. We prove some global shift invariance properties previously conjectured by other authors, and also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. In addition, strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a di usion equation (with multiplicative noise) through a Hopf{Cole transformation. Whereas the nearest-neighbor discretization passes the consistency tests, known examples in the literature do not. We propose a consistent and highly accurate scheme, and emphasize the importance of the Lyapunov functional as a natural starting point for real-space discretization. Also, in the light of these ndings, the mainstream opinion on the relevance of Galilean invariance and the uctuation{dissipation theorem (peculiar of 1D) is challenged [2,3,4].
Description92 diapositivas.-- Trabajo presentado al 12th International Workshop on Instabilities and Non-Equilibrium Structures celebrado en Viña del Mar (Chile) del 14 al 18 de diciembre de 2009.-- Presentado como contribuciones orales al "Dynamics Days Europe 2010" celebrado en Bristol (UK) del 6 al 10 de septiembre de 2010 y al "11th Granada Seminar on Computational and Statistical Physics" celebrado en Granada (España) del 13 al 17 de septiembre de 2010.
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