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Transmission delay times of localized waves
1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, The Netherlands.
Summary
Wave localization in disordered waveguides separates delay time into two contributions. This study analytically solves the single-channel case and approximates solutions for multiple channels, revealing correlations between reflection and transmission times.
Area of Science:
- Condensed matter physics
- Wave phenomena in disordered systems
- Quantum chaos
Background:
- Wave localization describes the confinement of waves in disordered media.
- Transmission delay time (tau) is crucial for understanding wave propagation.
- Disordered waveguides exhibit complex scattering behavior.
Purpose of the Study:
- To investigate the impact of wave localization on transmission delay time in disordered waveguides.
- To analyze the separation of delay time into contributions from waveguide ends.
- To derive the distribution function P(tau) for different numbers of propagating modes.
Main Methods:
- Analytical derivation of the delay time distribution for N=1 propagating mode.
- Heuristic approximation for the distribution function P(tau) for N>1 modes.
- Analysis of the relationship between reflection and transmission delay times.
Main Results:
- Wave localization separates delay time (tau) into two equivalent contributions (chi and chi(')) from waveguide ends.
- For N=1 mode, chi and chi(') equal half the reflection delay time.
- A strong correlation is found between long reflection delay times and the dominant transmission channel.
Conclusions:
- The study provides analytical and approximate solutions for delay time distributions in disordered waveguides.
- Wave localization significantly influences the nature and distribution of transmission delay times.
- Understanding these correlations is key for controlling wave transport in complex systems.