Escape time in anomalous diffusive media

Details Escape time in anomalous diffusive media Escape time in anomalous diffusive media

2001-02-22

arxiv.org/abs/cond-mat/0102412v1

Physics

Condensed Matter

Statistical Mechanics

to appear in PRE

Scientific paper

10.1103/PhysRevE.63.051109

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, 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 $\nu\neq 1$ 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.

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