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Fokker-Planck approach to non-Gaussian normal diffusion: Hierarchical dynamics for diffusing diffusivity.

Sumiyoshi Abe1

  • 1Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; Institute of Physics, Kazan Federal University, Kazan 420008, Russia; Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent, Tashkent 100095, Uzbekistan; and ESIEA, 9 Rue Vesale, Paris 75005, France.

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Summary
This summary is machine-generated.

A new theoretical framework explains non-Gaussian normal diffusion observed in heterogeneous systems. This model accurately describes "diffusing diffusivity" by analyzing fast and slow degrees of freedom.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Non-Gaussian normal diffusion is experimentally observed in various heterogeneous systems.
  • Understanding the underlying mechanisms of diffusion in complex environments is crucial.

Purpose of the Study:

  • To develop a theoretical framework for non-Gaussian normal diffusion.
  • To explain the phenomenon of "diffusing diffusivity".

Main Methods:

  • Derivation of a set of three equations from the Fokker-Planck equation.
  • Analysis of systems with dynamical structure and largely separated time scales.
  • Modeling the fast degree of freedom, slow degree of freedom, and their coupling.

Main Results:

  • The developed theoretical framework consistently describes non-Gaussian normal diffusion.
  • The model successfully explains the phenomenon of "diffusing diffusivity".

Conclusions:

  • The proposed theoretical framework provides a consistent explanation for non-Gaussian normal diffusion.
  • The approach highlights the importance of separated time scales and coupling between degrees of freedom in heterogeneous systems.