Escape time in anomalous diffusive media

Abstract

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation ${\partial }_t\rho ={\partial }_x[{\partial }_{x}U\rho ]+D{\partial }_x^2{\rho }^{\nu }$, where the potential of the drift, $U(x)$, presents a double-well and $D,\nu$ 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 $\nu \ne 1$ 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.

to appear in PRE

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