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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Ergodic property of random diffusivity system with trapping events.

Xudong Wang1, Yao Chen2

  • 1School of Science, Nanjing University of Science and Technology, Nanjing, 210094, P.R. China.

Physical Review. E
|February 23, 2022
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Summary

This study introduces a model for particle motion in complex media, combining random diffusivity and long trapping events. The findings reveal non-ergodicity in random diffusivity models, even for normal diffusion cases.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Brownian yet non-Gaussian dynamics are observed in biological and active matter systems.
  • Random diffusivity in inhomogeneous environments is a key explanation for these phenomena.

Purpose of the Study:

  • To model particle motion in complex media with both random diffusivity and long trapping events.
  • To derive and analyze the statistical properties of such anomalous diffusion.

Main Methods:

  • Utilizing a Langevin system with a random diffusivity and an α-stable subordinator (α<1).
  • Deriving general expressions for ensemble- and time-averaged mean-squared displacements.
  • Obtaining analytic expressions for the ergodicity breaking parameter and probability density function.

Main Results:

  • General expressions for mean-squared displacements were derived, depending on inverse subordinator and diffusivity values.
  • Analytic expressions for the ergodicity breaking parameter and probability density function were obtained for specific time-dependent diffusivities.
  • The model demonstrates non-ergodicity for all diffusivity types, including the normal diffusion critical case.

Conclusions:

  • The developed model captures anomalous diffusion in complex media.
  • The study confirms the non-ergodic nature of random diffusivity models.
  • These findings are relevant for understanding particle transport in heterogeneous environments.