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arXiv · 0712.0551

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

Takaaki Monnai·Ayumu Sugita·Katsuhiro Nakamura
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Abstract

We explore the diffusion process in the non-Markovian spatio-temporal noise.%the escape rate problem in the non-Markovian spatio-temporal random 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.

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Takaaki Monnai, Ayumu Sugita, Katsuhiro Nakamura. 2008-02-13. Diffusion in the Markovian limit of the spatio-temporal colored noise. https://doi.org/10.1209/0295-5075/84/20005

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