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Long jumps in the strong-collision model

Ferrando1, Montalenti, Spadacini

  • 1INFM and CFSBT/CNR, Dipartimento di Fisica dell' Universita di Genova, via Dodecaneso 33, 16146 Genova, Italy.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

We calculated the jump-length probability distribution for particles in a periodic potential using a strong-collision model. A refined analytical approximation accurately predicts particle behavior, aligning well with numerical data.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • Particle diffusion in periodic potentials is crucial for understanding various physical phenomena.
  • The strong-collision model simplifies complex interactions by assuming velocity reequilibration upon collision.
  • Understanding jump-length distributions is key to characterizing transport properties.

Purpose of the Study:

  • To calculate the jump-length probability distribution for a classical particle in a periodic potential.
  • To investigate the validity of a strong-collision model in this context.
  • To develop and compare analytical approximations with numerical results.

Main Methods:

  • Utilized the strong-collision model where particle velocity is reequilibrated after each collision.

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  • Employed the matrix-continued-fraction method for obtaining exact numerical results.
  • Developed two distinct analytical approximations for the jump-length distribution.

    • Main Results:

    • Obtained exact numerical solutions for the jump-length probability distribution.
    • Proposed a first analytical approximation assuming immediate retrapping in the initial cell.
    • Developed a second analytical approximation considering only energy-reducing collisions for retrapping.
    • The second analytical approximation demonstrated excellent agreement with numerical data.

    Conclusions:

    • The strong-collision model provides a viable framework for studying particle diffusion in periodic potentials.
    • A refined analytical approximation, focusing on effective retrapping collisions, accurately predicts particle diffusion behavior.
    • This work offers a computationally efficient method for analyzing transport in periodic systems.