Volume 89, Number 4, February 2010
|Number of page(s)||6|
|Published online||05 March 2010|
KPZ equation: Galilean-invariance violation, consistency, and fluctuation-dissipation issues in real-space discretization
Instituto de Física de Cantabria (UC and CSIC) - Avda. de los Castros, s/n, E-39005 Santander, Spain, EU
2 Instituto de Investigaciones Físicas Mar del Plata (UNMdP and CONICET) - Deán Funes 3350, B7602AYL Mar del Plata, Argentina
3 ICMAT (CSIC-UAM-UC3M-UCM), Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid - Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain, EU
Corresponding author: email@example.com
Accepted: 4 February 2010
Strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a diffusion 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 emphasize the importance of the Lyapunov functional as natural starting point for real-space discretization and, in the light of these findings, challenge the mainstream opinion on the relevance of Galilean invariance.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 64.60.Ht – Dynamic critical phenomena / 68.35.Ct – Interface structure and roughness
© EPLA, 2010
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