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Ballistic localization in quasi-one-dimensional waveguides with rough surfaces.
F M Izrailev1, J A Méndez-Bermúdez, G A Luna-Acosta
1Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 3, 2004
Summary
Eigenstates in rough waveguides exhibit unusual localization, defying classical predictions. These findings challenge standard statistical models for ballistic localization in such systems.
Area of Science:
- Physics
- Waveguide Theory
- Quantum Mechanics
Background:
- Understanding wave behavior in confined systems is crucial.
- Surface roughness significantly impacts wave propagation and localization.
- Classical models predict ergodic eigenstates in the high-energy limit.
Purpose of the Study:
- To investigate the structure of eigenstates in periodic quasi-one-dimensional waveguides with surface roughness.
- To analyze the convergence to the classical limit and localization properties.
- To evaluate the applicability of standard statistical approaches.
Main Methods:
- Analytical investigation of eigenstate structure.
- Numerical simulations of wave propagation.
- Analysis of localization in momentum and coordinate representations.
Main Results:
- A significant number of "regular" eigenstates were identified at high energies.
- Slow convergence to the expected ergodic classical limit was observed.
- Eigenstates from low-index transverse channels showed strong localization in momentum space and delocalization in coordinate space.
- These eigenstates displayed a "repulsion" effect from the rough surface.
Conclusions:
- The presence of regular eigenstates challenges the assumption of complete ergodicity in the classical limit.
- Standard statistical approaches for ballistic localization are likely inappropriate for these waveguide systems.
- The observed localization properties and surface repulsion necessitate new theoretical frameworks.