Microscopic theory of anomalous diffusion based on particle interactions

Lutsko, James
Boon, Jean-Pierre

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Publication date

August 2013

DOI

10.1103/PhysRevE.88.022108

Publisher

American Physical Society (APS)

ISSN

1539-3755

Abstract

We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavior is reflected not only in the mean squared displacement [r2(t)∼tγ with 0<γ≤1.5] but also in the existence of self-similar scaling solutions of the Fokker-Planck equation. We give a physical interpretation of sub- and superdiffusion in terms of the attractive and repulsive interactions between the diffusing particles and we discuss analytically the l...