Fractional Langevin equation to describe anomalous diffusion

Details Fractional Langevin equation to describe anomalous diffusion Fractional Langevin equation to describe anomalous diffusion

1999-07-30

arxiv.org/abs/chao-dyn/9908001v1

Physics

Condensed Matter

Statistical Mechanics

22 pages; presented on the 4th International Summer School/Conference "Let's Face Chaos through Nonlinear Dynamics", 28 June-1

Scientific paper

10.1143/PTPS.139.470

A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional time differential operators instead of usual ones is also proposed to describe anomalous diffusion processes. Such equation can be regarded as corresponding to systems with incomplete Hamiltonian chaos, and depending on the type of the relationship between the speed and coordinate of a particle yields either usual or fractional long-time behavior of diffusion. Correlations with the fractional Fokker-Planck equation are analyzed. Possible applications of the proposed equation beside anomalous diffusion itself are discussed.

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