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Dynamical continuous time random Lévy flights

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Abstract

The Lévy flights’ diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton’s Second Law while the nonlinear friction f(v) = − γ 0 v − γ 2 v 3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index μ = 2 case, it is still Brownian motion.

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Authors and Affiliations

  1. School of Science, Beijing Technology and Business University, Beijing, 100048, P.R. China

    Jian Liu

  2. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Jian Liu & Xiaosong Chen

Authors
  1. Jian Liu
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  2. Xiaosong Chen
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Correspondence to Jian Liu.

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Liu, J., Chen, X. Dynamical continuous time random Lévy flights. Eur. Phys. J. B 89, 64 (2016). https://doi.org/10.1140/epjb/e2016-60883-2

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  • DOI: https://doi.org/10.1140/epjb/e2016-60883-2

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