Dynamics of localization in a waveguide

Abstract

This is a review of the dynamics of wave propagation through a disordered N-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of a reflected pulse. The long-time dynamics is dominated by resonant transmission over length scales much larger than the localization length. The corresponding distribution of the Wigner-Smith delay times is the Laguerre ensemble of random-matrix theory. In the power spectrum the resonances show up as a 1/t^2 tail after N^2 scattering times. In the distribution of single-mode delay times the resonances introduce a dynamic coherent backscattering effect, that provides a way to distinguish localization from absorption.

18 pages including 8 figures; minor corrections

References in corpus (4)

• Statistics of energy levels and eigenfunctions in disordered systems
• Statistical Signatures of Photon Localization
• Imaginary Potential as a Counter of Delay Time for Wave Reflection from a 1D Random Potential
• High-frequency dynamics of wave localisation

Cited by in corpus (5)

• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Charge densities and charge noise in mesoscopic conductors
• Distribution of spectral linear statistics on random matrices beyond the large deviation function -- Wigner time delay in multichannel disordered wires
• Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity
• Time delay in 1D disordered media with high transmission