Abstract
We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external nonlinear force field. For the force-free case, the velocity damping follows the Mittag−Leffler relaxation and the diffusion is enhanced. The equation obeys the generalized Einstein relation, and its stationary solution is the Boltzmann distribution. Our results are compared to previous results on enhanced Lévy type of diffusion derived from stochastic collision models.
Keywords
Einstein relationBoltzmann equationPhysicsHeat equationDiffusionDiffusion equationClassical mechanicsRelaxation (psychology)Anomalous diffusionDistribution (mathematics)Statistical physicsParticle (ecology)Nonlinear systemField (mathematics)Mathematical physicsMathematical analysisMathematicsQuantum mechanics
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Publication Info
- Year
- 2000
- Type
- article
- Volume
- 104
- Issue
- 16
- Pages
- 3866-3874
- Citations
- 185
- Access
- Closed
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Cite This
Eli Barkai,
R. Silbey
(2000).
Fractional Kramers Equation.
The Journal of Physical Chemistry B
, 104
(16)
, 3866-3874.
https://doi.org/10.1021/jp993491m
Identifiers
- DOI
- 10.1021/jp993491m