Lévy walks in nonhomogeneous environments

Abstract

The Lévy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha >1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a nonhomogeneous trap distribution. The master equation is derived and solved in the asymptotic limit for a power-law form of the jumping rate. The relative density of resting and flying particles appears time-dependent and the asymptotic form of both distribution obey a stretched-exponential shape at large time. The diffusion properties are discussed and it is demonstrated that, due to the heterogeneous trap structure, the enhanced diffusion, observed for the homogeneous case, may turn to a subdiffusion. The density distributions and mean squared displacements are also evaluated from Monte Carlo simulations of individual trajectories.

12 pages, 3 figures

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Cited by in corpus (3)

• First-passage and first-hitting times of Levy flights and Levy walks
• Closed-form solutions for the Lévy-stable distribution
• Levy walks with variable waiting time: a ballistic case