Diffusion in the Markovian limit of the spatio-temporal colored noiseT. Monnai1, A. Sugita2 and K. Nakamura2, 3
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 in final form 4 September 2008; published October 2008
published online 6 October 2008
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.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.60.Cd - Classical transport.
02.50.Ey - Stochastic processes.
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