Escape time in anomalous diffusive media

Abstract

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t ρ= \partial_x[\partial_x Uρ] + D\partial^2_x ρ^ν$, where the potential of the drift, $U(x)$, presents a double-well and $D, ν$ are real parameters. For systems close to the steady state we obtain an analytical expression of the mean first passage time, yielding a generalization of Arrhenius law. Analytical predictions are in very good agreement with numerical experiments performed through integration of the associated Ito-Langevin equation. For $ν\neq 1$ important anomalies are detected in comparison to the standard Brownian case. These results are compared to those obtained numerically for initial conditions far from the steady state.