Anomalous diffusion and the first passage time problem

Details Anomalous diffusion and the first passage time problem Anomalous diffusion and the first passage time problem

2001-05-14

arxiv.org/abs/cond-mat/0105267v1

Phys. Rev. E62 (2000) 120-133

Physics

Condensed Matter

Statistical Mechanics

25 pages, 4 figures

Scientific paper

10.1103/PhysRevE.62.120

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.

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