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 $1/t^{\alpha }$ 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 $\alpha$ 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.

9 pages, 6 figures. Revised text

References in corpus (6)

• Anderson Transitions
• Dynamics of Anderson localization in open 3D media
• Dynamics of weakly localized waves
• A random matrix approach to detect defects in a strongly scattering polycrystal: how the memory effect can help overcome multiple scattering
• Microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size
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Cited by in corpus (8)

• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current
• Quantum criticality in the disordered Aubry-André model
• Kibble-Zurek scaling in one-dimensional localization transitions
• Spinful Aubry-Andre model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility