Noise-induced escape rate over a potential barrier: Results for general noise

We extend a recent instanton calculation of the escape rate Γ over a one-dimensional potential barrier in the weak-noise limit (D→0), from the case where the noise is Gaussian and exponentially correlated to a more general process. Specifically, the system we initially consider consists of a Langevin equation ẋ=-V’(x)+ξ, where ξ is a Gaussian noise with zero mean and correlator 〈ξ(t)ξ(t’)〉=(D/τ)C(‖t-t’‖/τ), τ being the noise correlation time. Using a path-integral formulation of this process, we find that, in the weak-noise limit, Γ∼exp(-S/D) and calculate S order ${\tau }^6$ for an arbitrary double-well potential. The extension to non-Gaussian processes is briefly discussed.