Bistable Flow Driven by Coloured Gaussian Noise: A Critical Case Study

Hanggi, P. and Marchesoni, F. and Grigolini, P. (1984) Bistable Flow Driven by Coloured Gaussian Noise: A Critical Case Study. (Preprint)

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Abstract

A one dimensional flow driven by additive Gaussian noise is considered. Possible pitfalls in the use of Langevin equations of non-Markovian processes are identified. In particular, the stationarity of the random force in a non-Markovian Langevin equation does not imply that the dynamics of the non-Markovian process is consistent with an initial stationary preparation scheme. The small relaxation time Fokker-Planck approximation schemes put forward in the recent literature are applied and it is pointed out that those schemes may lead to unreliable predictions. The results for the activation rate as evaluated from the approximative Fokker-Planck schemes does not coincide in leading order in τ (Arrhenius factor) with a computer simulation for small noise intensity: thus showing that the wings of the stationary probability p̄(x) are in leading order in τ not recovered from the approximative Fokker-Planck schemes.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 06 Jul 2018 10:44
Last Modified: 24 Jul 2018 11:41
URI: http://dair.dias.ie/id/eprint/859

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