Time-dependent reflection at the localization transition

TL;DR

This paper investigates how wave reflection decay behaves near the Anderson localization transition using the Aubry-André model, revealing a slowdown in decay rate close to the critical point.

Contribution

It demonstrates that near the localization transition, the decay exponent decreases below known values, highlighting a new dynamic regime in wave reflection.

Findings

Decay exponent $eta$ becomes smaller near the transition

Slower power-law decay than in localized or diffusive regimes

Provides insight into wave dynamics at criticality

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 $1/t^{\alpha}$ in the long-time limit. Using the one-dimensional Aubry-Andr\'{e} model, we show that in the vicinity of the critical point of Anderson localization transition, the decay slows down and the power-law exponent $\alpha$ becomes smaller than both $\alpha = 2$ found in the Anderson localization regime and $\alpha = 3/2$ expected for a one-dimensional random walk of classical particles.