Fractional Brownian motion in presence of two fixed adsorbing boundaries

Details Fractional Brownian motion in presence of two fixed adsorbing boundaries Fractional Brownian motion in presence of two fixed adsorbing boundaries

2008-01-04

arxiv.org/abs/0801.0676v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, submitted to J.Phys.A

Scientific paper

We study the long-time asymptotics of the probability P_t that the Riemann-Liouville fractional Brownian motion with Hurst index H does not escape from a fixed interval [-L,L] up to time t. We show that for any H \in ]0,1], for both subdiffusion and superdiffusion regimes, this probability obeys \ln(P_t) \sim - t^{2 H}/L^2, i.e. may decay slower than exponential (subdiffusion) or faster than exponential (superdiffusion). This implies that survival probability S_t of particles undergoing fractional Brownian motion in a one-dimensional system with randomly placed traps follows \ln(S_t) \sim - n^{2/3} t^{2H/3} as t \to \infty, where n is the mean density of traps.

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