Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing a metastable potential and its predictions are in excellent agreement with numerical simulations. The results exhibit the anomalies due to the nonlinearity in W that the escape rate grows with D and drops as mu becomes large at a fixed D. Indeed, particles in the subdiffusive media (mu>1) can escape over the barrier only when D is above a critical value, while this confinement does not exist in the superdiffusive media (mu < 1).