Local diffusion theory of localized waves in open media

TL;DR

This paper presents a first-principles analysis of static wave transport in open, disordered media, revealing novel diffusive behaviors dominated by resonant transmissions and challenging existing localization theories.

Contribution

It introduces a new understanding of wave diffusion in open media, highlighting the importance of resonant transmissions and testing the limits of existing localization theories.

Findings

Resonant transmissions dominate wave transport in open media.

Standard localization theory is only valid when resonant transmissions are negligible.

Numerical simulations confirm the analytical predictions.

Abstract

We report a first-principles study of static transport of localized waves in quasi-one-dimensional open media. We found that such transport, dominated by disorder-induced resonant transmissions, displays novel diffusive behavior. Our analytical predictions are entirely confirmed by numerical simulations. We showed that the prevailing self-consistent localization theory [van Tiggelen, {\it et. al.}, Phys. Rev. Lett. \textbf{84}, 4333 (2000)] is valid only if disorder-induced resonant transmissions are negligible. Our findings open a new direction in the study of Anderson localization in open media.