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Subdiffusion and localization in the one-dimensional trap model.

E M Bertin1, J-P Bouchaud

  • 1Commissariat à l'Energie Atomique, Service de Physique de l'Etat Condensé, 91191 Gif-sur-Yvette Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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This study reveals that anomalous diffusion in generalized exponential trap models exhibits distinct localization properties and aging behaviors. The research highlights discrepancies between dynamical and equilibrium states, indicating complex scaling in these systems.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • The exponential trap model is crucial for understanding anomalous diffusion.
  • Investigating its one-dimensional generalization provides insights into complex dynamics.
  • Localization and aging phenomena are key characteristics of disordered systems.

Purpose of the Study:

  • To analyze the diffusion front and localization properties in a 1D exponential trap model.
  • To investigate the aging behavior and identify multiple time scales.
  • To compare dynamical properties with equilibrium states.

Main Methods:

  • Employed numerical simulations to model the system's behavior.
  • Utilized analytical approximations for theoretical insights.

Related Experiment Videos

  • Calculated dynamical participation ratios and two-time correlation functions.

    • Main Results:

    • The average diffusion front shows a distinct asymptotic shape in the subdiffusive phase.
    • Dynamical participation ratios are finite but differ from equilibrium values, indicating no exact partial equilibrium.
    • Two distinct aging behaviors ('sub aging' and 'full aging') were observed, revealing two diverging time scales.

    Conclusions:

    • The study clarifies the complex localization and aging dynamics in generalized exponential trap models.
    • Discrepancies between dynamical and equilibrium properties are physically explained.
    • The findings predict multiple time scalings, offering a deeper understanding of anomalous transport.