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Anomalous diffusion of particles with inertia in external potentials
1Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, D-48149 Münster, Germany.
The Journal of Physical Chemistry. B
|October 24, 2007
Summary
A new Kramers-Fokker-Planck equation models anomalous diffusion. External potentials and damping cause subdiffusion, with particles localizing over time.
Area of Science:
- Physics
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Anomalous diffusion describes particle movement deviating from standard Brownian motion.
- Kramers-Fokker-Planck equations are fundamental for modeling diffusion processes.
- External potentials and damping significantly influence particle dynamics.
Purpose of the Study:
- To incorporate harmonic potentials and velocity-dependent damping into a novel Kramers-Fokker-Planck equation.
- To analyze the resulting anomalous diffusion behavior.
- To investigate the long-time asymptotic behavior of the system.
Main Methods:
- Modification of the Kramers-Fokker-Planck equation.
- Derivation of exact moment relations for specific potentials and damping.
- Analysis of asymptotic behavior for long time scales.
Main Results:
- The inclusion of a bounding potential leads to subdiffusive behavior.
- Velocity-dependent damping also induces subdiffusion.
- The combined effect of potential and damping results in particle localization.
Conclusions:
- The proposed Kramers-Fokker-Planck model effectively describes anomalous diffusion under external influences.
- Both bounding potentials and damping contribute to subdiffusive particle transport.
- Synergistic effects lead to long-term particle localization, a significant deviation from standard diffusion.
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