Katzav Eytan, Schwartz Moshe
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jul;70(1 Pt 1):011601. doi: 10.1103/PhysRevE.70.011601. Epub 2004 Jul 2.
In this paper we discuss the well known Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise. We use a self-consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the behavior of the dynamic structure factor Phiq(t) as a function of time. The approach we use here generalizes the well known self-consistent expansion (SCE) that was used successfully in the case of the KPZ equation driven by white noise, but unlike SCE, it is not based on a Fokker-Planck form of the KPZ equation, but rather on its Langevin form. A comparison to two other analytical methods, as well as to the only numerical study of this problem is made, and a need for an updated extensive numerical study is identified. We also show that a generalization of this method to any spatiotemporal correlations in the noise is possible, and two examples of this kind are considered.
