Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach
- 3 May 1999
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 82 (18) , 3563-3567
- https://doi.org/10.1103/physrevlett.82.3563
Abstract
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.Keywords
This publication has 30 references indexed in Scilit:
- NMR microscopy of pore-space backbones in rock, sponge, and sand in comparison with random percolation model objectsPhysical Review E, 1997
- Subdiffusion and Anomalous Local Viscoelasticity in Actin NetworksPhysical Review Letters, 1996
- Non-Gaussian Transport Measurements and the Einstein Relation in Amorphous SiliconPhysical Review Letters, 1996
- The Fokker-Planck EquationPublished by Springer Nature ,1996
- Fractional model equation for anomalous diffusionPhysica A: Statistical Mechanics and its Applications, 1994
- Fractional diffusion and wave equationsJournal of Mathematical Physics, 1989
- Stochastic pathway to anomalous diffusionPhysical Review A, 1987
- Analytical Solutions for Diffusion on Fractal ObjectsPhysical Review Letters, 1985
- Anomalous transit-time dispersion in amorphous solidsPhysical Review B, 1975
- Fractional Brownian Motions, Fractional Noises and ApplicationsSIAM Review, 1968