title: Kramers' law for a bistable system with time-delayed noise.
abstract: 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.
authors.affiliation: Tyndall National Institute, Lee Maltings, Cork, Ireland.
authors.forename: D
authors.initials: D
authors.lastname: Goulding
authors.forename: S
authors.initials: S
authors.lastname: Melnik
authors.forename: D
authors.initials: D
authors.lastname: Curtin
authors.forename: T
authors.initials: T
authors.lastname: Piwonski
authors.forename: J
authors.initials: J
authors.lastname: Houlihan
authors.forename: J P
authors.initials: JP
authors.lastname: Gleeson
authors.forename: G
authors.initials: G
authors.lastname: Huyet