Memory effect on thermally activated escape rates

Non-Markovian thermal Brownian motion of a particle over a barrier is studied using thermal noise with a small but finite bath-memory correlation time. Starting from the corresponding non-Markovian Smoluchowski master equation, valid in the over-damped limit, the rate of escape λ is evaluated, and it is shown that a renormalization of the bare damping occurs. The modeling of the rate λ for a special class of bistable, driven non-Markovian nonequilibrium systems is sketched.