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

Goulding, D. and Melnik, S. and Curtin, D. and Piwonski, T. and Houlihan, John and Gleeson, J. P. and Huyet, G. (2007) Kramers' law for a bistable system with time-delayed noise. Physical Review E, 76 (3). p. 5. ISSN 15502376

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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 < 2 tau 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.

Item Type: Article
Additional Information: ISI Document Delivery No.: 215CL Times Cited: 7 Cited Reference Count: 22 Goulding, D. Melnik, S. Curtin, D. Piwonski, T. Houlihan, J. Gleeson, J. P. Huyet, G. AMER PHYSICAL SOC COLLEGE PK Part 1
Departments or Groups: Optics Research Group
Divisions: School of Science > Department of Computing, Maths and Physics
Depositing User: John Houlihan
Date Deposited: 20 Nov 2012 11:07
Last Modified: 22 Aug 2016 10:26

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