David Hochberg, Carmen Molina-Paris, Juan Perez-Mercader, Matt Visser
Published 1999-04-28, updated 2000-11-27Version 2
A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions.
Comments: V2 --- 6 pages, LaTeX 209, ReV_TeX 3.2. Title changed, presentation clarified, additional discussion added, references updated. No significant changes in physics conclusions. This version to appear in Physics Letters A
Journal: Phys.Lett.A278:177-183,2001
KPZ equation with correlated noise: emergent symmetries and non-universal observables
Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media
Anomaly in Numerical Integrations of the KPZ Equation and Improved Discretization
