Kramers problem for overdamped systems driven by correlated noise: Results for vanishing diffusion coefficients

We have obtained results for the activation energy in bistable overdamped systems driven by colored noise. Our results cover the region of small diffusion coefficients and small to large correlation times. A scaling relation between the escape rate from one attractor to the other and the diffusion coefficient allows us to obtain results for the activation energy in the limit of vanishingly small diffusion coefficients. Numerical results for both the activation energy and the mean first-passage time are compared with theoretical predictions.