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Driven classical diffusion with strong correlated disorder.

Leonid P Pryadko1, Jing-Xian Lin

  • 1Department of Physics, University of California, Riverside, 92521, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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We discovered a crossover regime in driven classical diffusion with potential disorder. Mobility values change exponentially between low and high driving forces, with power-law or linear dependencies for correlated disorder.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Nonlinear Dynamics

Background:

  • Classical diffusion in disordered systems is fundamental to understanding transport phenomena.
  • The influence of driving forces on particle mobility in the presence of quenched disorder is complex.
  • Previous studies often focused on asymptotic regimes (very low or very high driving forces).

Purpose of the Study:

  • To identify and characterize the crossover regime in driven classical diffusion with strong potential disorder.
  • To investigate the dependence of particle mobility on the driving force within this crossover.
  • To analyze the impact of disorder correlation length on the mobility-force relationship.

Main Methods:

  • Theoretical analysis of driven classical diffusion.

Related Experiment Videos

  • Investigation of systems with quenched potential disorder V(x).
  • Mathematical derivation of mobility (mu) as a function of driving force (F) for different disorder correlation properties.

    • Main Results:

    • A distinct crossover regime for mobility (mu(F)) was identified between low and high driving forces (F), exhibiting exponential differences.
    • For power-law correlated disorder ( ~ |x-y|^(-n)), the crossover shows a power-law dependence: ln(mu(F)) ~ F^(n/(n+1)).
    • For finite-range disorder (n=infinity), the dependence becomes linear, described as 'logarithmic susceptibility'.

    Conclusions:

    • The crossover regime significantly impacts the understanding of transport in disordered systems.
    • Disorder correlation plays a crucial role in determining the functional form of mobility dependence on driving force.
    • The findings provide a more complete picture of driven diffusion beyond asymptotic limits.