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 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.
Goulding
D
D
Tyndall National Institute, Lee Maltings, Cork, Ireland.
Melnik
S
S
Curtin
D
D
Piwonski
T
T
Houlihan
J
J
Gleeson
J P
JP
Huyet
G
G