Time-dependent reflection at the localization transition

Abstract

A short quasi-monochromatic wave packet incident on a semi-infinite disordered medium gives rise to a reflected wave. The intensity of the latter decays as a power law $1/t^α$ in the long-time limit. Using the one-dimensional Aubry-André model, we show that in the vicinity of the critical point of Anderson localization transition, the decay slows down and the power-law exponent $α$ becomes smaller than both $α= 2$ found in the Anderson localization regime and $α= 3/2$ expected for a one-dimensional random walk of classical particles.