Instanton calculation of the escape rate for activation over a potential barrier driven by colored noise

In the weak noise limit (D0), the escape rate over a one-dimensional potential barrier is exp(-SD). Here S is calculated exactly by identifying appropriate instanton solutions in a path-integral formulation of the Langevin equation. For the "colored noise" problem, defined by the noise correlator (t)(t)=(D)exp{-|t-t|}, the instanton satisfies a fourth-order, nonlinear, ordinary differential equation which can be readily solved numerically. Analytical results are derived for small and large. © 1989 The American Physical Society.