Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach

被引：684

作者：

Metzler, R ^{[1
]}

Barkai, E

Klafter, J

机构：

[1] Tel Aviv Univ, Sch Chem, IL-69978 Tel Aviv, Israel

[2] Tel Aviv Univ, Sch Phys, IL-69978 Tel Aviv, Israel

来源：

PHYSICAL REVIEW LETTERS | 1999年 / 82卷 / 18期

关键词：

D O I：

10.1103/PhysRevLett.82.3563

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We introduce a fractional Fokker-Planck equation describing the stochastic evolution of a particle under the combined influence of an external, nonlinear force and a thermal heat bath. For the force-free case, a subdiffusive behavior is recovered. The equation is shown to obey generalized Einstein relations, and its stationary solution is the Boltzmann distribution. The relaxation of single modes is shown to follow a Mittag-Leffler decay. We discuss the example of a particle in a harmonic potential. [S0031-9007(99)09071-7].

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页码：3563 / 3567

页数：5

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