Kardar-Parisi-Zhang equation with temporally correlated noise: A self-consistent approach

A time-dependent self-consistent approach was developed to deal with the Kardar-Parisi-Zhang (KPZ) equation driven by a temporally correlated noise. It was found that when temporally correlated noise is present in the system, then slow relaxations of various time-dependent quantities should control the long-time behavior. It was also found that the KPZ equation has both a strong-coupling and a weak-coupling solution. The results indicate towards the advantage in using the self-consistent approach as it can be generalized in a simple way to discuss noise with arbitrary spatiotemporal correlations.