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Fractional generalized Langevin equation approach to single-file diffusion

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  • Eab, C.H.
  • Lim, S.C.

Abstract

Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short and long time behavior for the mean square displacement of single-file diffusion when appropriate choice of parameters associated with fractional generalized Langevin equation are used. By considering some special cases of the fractional generalized Langevin equation, a new class of closed analytic expressions for the mean square displacement of single-file diffusion can be obtained. The effective Fokker–Planck equation associated with single-file diffusion is briefly considered.

Suggested Citation

  • Eab, C.H. & Lim, S.C., 2010. "Fractional generalized Langevin equation approach to single-file diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2510-2521.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:13:p:2510-2521
    DOI: 10.1016/j.physa.2010.02.041
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    References listed on IDEAS

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    1. Wang, K.G & Tokuyama, M, 1999. "Nonequilibrium statistical description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 341-351.
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    Cited by:

    1. Dumitru Baleanu & Rahmat Darzi & Bahram Agheli, 2020. "Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Zheng, Yunying & Zhao, Zhengang & Cui, Yanfen, 2019. "The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 257-269.

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