Kramers' law for a bistable system with time-delayed noise

We demonstrate that the classical Kramers' escape problem can be extended to describe a bistable system under the influence of noise consisting of the superposition of a white Gaussian noise with the same noise delayed by time tau . The distribution of times between two consecutive switches dec...

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Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 76; no. 3 Pt 1; p. 031128
Main Authors Goulding, D, Melnik, S, Curtin, D, Piwonski, T, Houlihan, J, Gleeson, J P, Huyet, G
Format Journal Article
LanguageEnglish
Published United States 01.09.2007
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Summary:We demonstrate that the classical Kramers' escape problem can be extended to describe a bistable system under the influence of noise consisting of the superposition of a white Gaussian noise with the same noise delayed by time tau . The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<tau and tau<t<2tau are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than tau, the delayed noise acquires a nonzero mean value and becomes negatively autocorrelated. To account for these effects we define an effective potential and an effective diffusion coefficient of the delayed noise.
ISSN:1539-3755
DOI:10.1103/PhysRevE.76.031128