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Fractional Fokker-Planck equations for subdiffusion with space- and time-dependent forces
B I Henry1, T A M Langlands, P Straka
1Department of Applied Mathematics, University of New South Wales, Sydney NSW, Australia. B.Henry@unsw.edu.au
Physical Review Letters
|January 15, 2011
Summary
We derived a fractional Fokker-Planck equation for subdiffusion, applicable to complex systems with time-dependent forces. This equation models particle movement influenced by Boltzmann weights and continuous time random walks.
Area of Science:
- Physics
- Statistical Mechanics
- Non-equilibrium Systems
Background:
- Subdiffusion is a key transport mechanism in complex systems.
- Continuous time random walks (CTRWs) model anomalous diffusion.
- Force fields significantly influence particle dynamics.
Purpose of the Study:
- Derive a fractional Fokker-Planck equation for subdiffusion.
- Incorporate space- and time-dependent force fields.
- Analyze systems biased by Boltzmann weights.
Main Methods:
- Utilizing power law waiting time continuous time random walks.
- Deriving the governing equation from a generalized master equation.
- Establishing equivalence to a subordinated stochastic Langevin equation.
Main Results:
- A fractional Fokker-Planck equation for subdiffusion was successfully derived.
- The equation accounts for general space- and time-dependent force fields.
- The derived equation is equivalent to a subordinated stochastic Langevin equation.
Conclusions:
- The derived fractional Fokker-Planck equation provides a powerful tool for modeling subdiffusion.
- This framework is applicable to diverse physical systems with complex driving forces.
- The equivalence to a Langevin equation offers insights into the underlying stochastic processes.
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