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Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach
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.
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Citations
Cites
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
Cole, K. S., & Cole, R. H. (1941) · The Journal of Chemical Physics · doi:10.1063/1.1750906 · Cited by 10,152
Cited by
Metzler, R., Jeon, J.-H., Cherstvy, A. G., & Barkai, E. (2014) · Phys. Chem. Chem. Phys. · doi:10.1039/c4cp03465a · Cited by 1,765
Self-citationThe ergodic side of the many‐body localization transition
Luitz, D. J., & Lev, Y. B. (2017) · Annalen der Physik · doi:10.1002/andp.201600350 · Cited by 308
Metadata
- Authors
- Metzler, R., Barkai, E., & Klafter, J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1999-05-03
- Volume
- 82
- Issue
- 18
- Pages
- 3563-3567
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2045514685
- Cited by
- 777
- References
- 1
- FWCI
- 64.06
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach. https://app.cochat.ai/papers/10.1103/physrevlett.82.3563
- The paper
- Metzler, R., Barkai, E., & Klafter, J. (1999). Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach. Physical Review Letters. https://doi.org/10.1103/physrevlett.82.3563
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