Dynamics of localization in a waveguide

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.