KPZ equation: Galilean-invariance violation, consistency, and fluctuation-dissipation issues in real-space discretization

H. S. WIO; J. A. REVELLI; R. R. DEZA; C. ESCUDERO; M. S. DE LA LAMA

EUROPHYSICS LETTERS

EPL ASSOCIATION

Lugar: Les Ulis; Año: 2010 vol. 89 p. 40008 - 40008

0295-5075

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.