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Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic
L S Froufe-Pérez1, M Yépez, P A Mello
1Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
Summary
We developed a diffusion equation for wave scattering in disordered waveguides, showing universal statistical properties depend only on mean free paths. Numerical simulations confirm results, offering insights into transport properties.
Area of Science:
- Condensed Matter Physics
- Wave Phenomena
- Statistical Mechanics
Background:
- Wave scattering in disordered systems is crucial for understanding transport properties.
- Previous models often neglected particle energy or simplified scattering mechanisms.
Purpose of the Study:
- To derive and analyze the statistical properties of wave scattering in disordered waveguides.
- To develop a universal model applicable in the dense-weak-scattering limit.
- To account for incident particle energy in scattering calculations.
Main Methods:
- A potential model using idealized delta slices to represent scattering units.
- Derivation of statistical properties for a waveguide 'building block'.
- Development of a diffusion equation in transfer matrix space.
- Numerical simulation technique: 'random walk in the transfer matrix space'.
Main Results:
- Universal statistical properties emerge in the dense-weak-scattering limit, depending solely on mean free paths.
- A diffusion equation accurately describes the evolution of transport properties with waveguide length.
- Numerical simulations show excellent agreement with microscopic calculations for both bulk and surface disorder.
Conclusions:
- The study establishes a generalized central limit theorem for wave scattering in disordered waveguides.
- The developed diffusion equation and numerical methods provide a robust framework for analyzing transport phenomena.
- The findings are broadly applicable, considering incident particle energy and various disorder types.
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