Diffusion in the Markovian limit of the spatio-temporal colored noise

¹  Department of Applied Physics, Waseda University - 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
²  Department of Applied Physics, Osaka City University - 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
³  Heat Physics Department, Uzbek Academy of Sciences - 28 Katartal Str., 700135 Tashkent, Uzbekistan

Received: 17 April 2008
Accepted: 4 September 2008

Abstract

We explore the diffusion process in the non-Markovian spatio-temporal noise. There is a non-trivial short-memory regime, i.e., the Markovian limit characterized by a scaling relation between the spatial and temporal correlation lengths. In this regime, a Fokker-Planck equation is derived by expanding the trajectory around the systematic motion and the non-Markovian nature amounts to the systematic reduction of the potential. For a system with the potential barrier, this fact leads to the renormalization of both the barrier height and collisional prefactor in the Kramers escape rate, with the resultant rate showing a maximum at some scaling limit.