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Diffusion in lattice Lorentz gases with a percolation threshold.

L Acedo1, A Santos

  • 1Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study introduces a new mean-field approximation for diffusion in lattice Lorentz gases. The proposed method accurately predicts diffusion coefficients and percolation thresholds, outperforming the repeated ring approximation.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Transport Phenomena

Background:

  • Lattice Lorentz gases model particle transport with stochastic scatterers.
  • Understanding diffusion coefficients and percolation thresholds is crucial for these systems.
  • Existing approximations like the repeated ring approximation (RRA) have limitations.

Purpose of the Study:

  • To propose a novel mean-field approximation for the diffusion coefficient in lattice Lorentz gases.
  • To relate the diffusion coefficient to the first return probability using an effective ring operator.
  • To develop a renormalization scheme for approximating the first return probability.

Main Methods:

  • Developed a mean-field approximation for the diffusion coefficient in the low-density limit.

Related Experiment Videos

  • Utilized an effective ring operator connecting diffusion to first return probability on a Cayley tree.
  • Constructed a renormalization scheme for approximate first return probability calculation.
  • Compared theoretical predictions with computer simulations for models with backscatterers.

    • Main Results:

    • The proposed mean-field approximation shows good agreement with computer simulation results.
    • The approximation accurately predicts the vanishing of the diffusion coefficient beyond the percolation threshold.
    • The repeated ring approximation (RRA) fails to accurately predict the percolation threshold.

    Conclusions:

    • The novel mean-field approximation provides a reliable method for studying diffusion in lattice Lorentz gases.
    • This approach offers improved accuracy over the RRA, particularly near percolation thresholds.
    • The study highlights the importance of accurate first return probability calculations for transport phenomena.