Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-09-11
Phys. Rev. E 70, 011601 (2004)
Physics
Condensed Matter
Statistical Mechanics
28 pages, 2 figures
Scientific paper
10.1103/PhysRevE.70.011601
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 $\Phi_q(t)$ 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 spatio-temporal correlations in the noise is possible, and two examples of this kind are considered.
Katzav Eytan
Schwartz Moshe
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