Escape time in anomalous diffusive media

Abstract

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation ∂tρ = ∂x[∂xU ρ] + D∂ 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 = 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.

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Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations

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