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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Diffusion processes are fundamental in various scientific fields.
  • Heterogeneous environments introduce complexities in diffusion dynamics.
  • Disorder, both annealed and quenched, significantly impacts particle transport.

Purpose of the Study:

  • To analyze noisy heterogeneous diffusion with position-dependent diffusivity.
  • To investigate the effects of annealed and quenched disorder on diffusion.
  • To characterize the statistical properties of anomalous diffusion.

Main Methods:

  • Theoretical modeling of diffusion with position-dependent diffusivity D(x) ∼ D0|x|(α0).
  • Analysis of annealed disorder (α0(t)) and quenched disorder.
  • Calculation of ensemble and time-averaged mean squared displacement (MSD).
  • Investigation of ergodicity breaking parameter and higher-order moments.

Main Results:

  • Annealed disorder modifies long-time scaling of ensemble MSD and time-averaged MSD amplitude.
  • Quenched disorder leads to effective Brownian motion after domain jumps in stratified media.
  • Disorder strength critically influences diffusion behavior and statistical observables.

Conclusions:

  • The study provides a comprehensive analysis of anomalous diffusion under disorder.
  • Understanding these effects is crucial for fields ranging from biophysics to materials science.
  • The findings offer insights into the statistical mechanics of complex transport phenomena.