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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
Summary
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.
- 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.