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Related Experiment Videos

Generalized Landauer equation: absorption-controlled diffusion processes.

S Godoy1, L S García-Colín, V Micenmacher

  • 1Facultad de Ciencias, Universidad Nacional Autónoma de México, México 04510 Distrito Federal, Mexico. sgs@hp.fciencias.unam.mx

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study derives a formula for particle multiple scattering through materials, linking it to single-scattering properties. The findings unify transport phenomena like electron conduction, neutron diffusion, and photon absorption.

Area of Science:

  • Physics
  • Materials Science
  • Transport Phenomena

Background:

  • The Boltzmann transport equation describes particle behavior in materials.
  • Understanding multiple scattering is crucial for various physical processes.
  • Existing models often simplify scattering or absorption effects.

Purpose of the Study:

  • To derive an exact expression for one-dimensional Boltzmann multiple-scattering coefficients.
  • To relate these coefficients to single-scattering cross sections, including absorption.
  • To unify diverse transport phenomena under a single theoretical framework.

Main Methods:

  • Derivation of exact multiple-scattering coefficients using the Boltzmann equation.
  • Expressing coefficients in terms of single-scattering cross section and absorption.

Related Experiment Videos

  • Analyzing limiting cases for different particle types and media.

    • Main Results:

    • Obtained exact one-dimensional multiple-scattering coefficients.
    • Recovered the Landauer result for non-absorbing metals.
    • Modified Landauer's formula for weakly absorbing media (e.g., neutrons).
    • Recovered the Lambert-Beer equation for strongly absorbing media (e.g., photons).

    Conclusions:

    • The derived formula provides a unified description of particle transport with scattering and absorption.
    • The results highlight the connection between absorption-controlled diffusion and established physical laws.
    • This framework offers insights into electron, neutron, and photon transport phenomena.