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Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies

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Fractional Fokker-Planck subdiffusion in alternating force fields.

E Heinsalu¹, M Patriarca, I Goychuk

¹National Institute of Chemical Physics and Biophysics, Rävala 10, Tallinn 15042, Estonia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 13, 2009

Summary

A new study shows that time-periodic forces do not alter anomalous diffusion scaling in biased subdiffusion systems. However, in unbiased systems, these forces can significantly enhance the subdiffusion coefficient.

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Area of Science:

Physics
Statistical Mechanics
Non-equilibrium Systems

Background:

Subdiffusion describes anomalous transport phenomena where particles spread slower than Brownian motion.
Continuous Time Random Walks (CTRW) provide a framework for modeling subdiffusion.
Fractional Fokker-Planck equations are used to describe subdiffusion dynamics.

Purpose of the Study:

To derive and analyze the fractional Fokker-Planck equation for subdiffusion in time-dependent force fields.
To investigate the impact of a time-periodic rectangular force on subdiffusion dynamics.
To compare the effects of such forces in biased versus unbiased systems.

Main Methods:

Derivation of the fractional Fokker-Planck equation from CTRW models.
Application of the derived equation to subdiffusion under a time-periodic rectangular force.
Analysis of scaling relations for anomalous current and diffusion in the long-time limit.

Main Results:

The fractional Fokker-Planck equation is derived and its limitations discussed.
In biased subdiffusion, a time-periodic force does not affect the universal scaling between anomalous current and diffusion.
In unbiased subdiffusion, the subdiffusion coefficient can be significantly enhanced by the periodic force, showing a zero-frequency response.

Conclusions:

Time-periodic forces have distinct effects on biased and unbiased subdiffusion.
Biased subdiffusion dynamics exhibit immunity to periodic driving in the long-time limit regarding scaling relations.
Unbiased subdiffusion can exhibit resonant enhancement of the diffusion coefficient in response to periodic driving.