2003/09/30 by Eytan Katzav, Moshe Schwartz · 1 citation
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Climate variability and models #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.70.011601
published as Phys. Rev. E 70, 011601 (2004) · 28 pages, 2 figures
arxiv created 2004/01/11 · openalex publication_date 2004/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.