The Kardar-Parisi-Zhang Equation with Temporally Correlated Noise - A Self Consistent Approach

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.