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

Goulding, D. and Melnik, S. and Curtin, D. and Piwonski, T. and Houlihan, J. and Gleeson, J. P. and Huyet, G. (2007) Kramers' law for a bistable system with time-delayed noise. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 76 (3). ISSN 1539-3755

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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 τ. The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<τ and τ<t<2τ are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than τ, 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
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/3100/3109
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Depositing User: Admin SSL
Date Deposited: 19 Oct 2022 23:07
Last Modified: 07 Jun 2023 18:44

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