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Mechanical model of normal and anomalous diffusion.

H Kunz1, R Livi, A Süto

  • 1Institut de Physique Theorique, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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We investigated charged particle motion in a disordered 1D system. Above a critical electric field, normal diffusion emerges, while at the threshold, anomalous diffusion signals a transition from conduction to localization.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Charged particle dynamics in disordered media are crucial for understanding transport phenomena.
  • Quenched disorder can lead to complex behaviors like localization and anomalous diffusion.
  • Previous models often rely on time-dependent forces, limiting applicability.

Purpose of the Study:

  • To investigate the overdamped dynamics of a charged particle driven by a uniform electric field in a 1D random sequence of scatterers.
  • To derive analytic expressions for mean velocity and velocity power spectrum.
  • To explore the emergence of normal and anomalous diffusion in a purely mechanical model with quenched disorder.

Main Methods:

  • Analytical derivation of mean velocity and velocity power spectrum for a charged particle in a 1D disordered system.

Related Experiment Videos

  • Analysis of particle dynamics under an external uniform electric field.
  • Investigation of diffusion properties (normal and anomalous) and their relation to field strength and disorder.

    • Main Results:

    • Analytic expressions for mean velocity and velocity power spectrum were obtained.
    • Above a threshold electric field, normal diffusion is superimposed on ballistic motion.
    • At the threshold field, a transition from conduction to localization is accompanied by anomalous diffusion.

    Conclusions:

    • A purely mechanical model with quenched disorder can exhibit both normal and anomalous diffusion without time-dependent stochastic forces.
    • Anomalous diffusion emerges as a critical property at the transition between conduction and localization.
    • The findings have implications for understanding particle segregation in flow systems, analogous to motion on an inclined rough surface.