Crossover Between Quantum and Classical Waves and High Frequency Localization Landscapes

TL;DR

This paper extends the localization landscape theory to high-frequency classical waves by transforming the wave equation into a Schrödinger form, enabling efficient prediction of localized modes in complex media.

Contribution

It introduces a method to adapt the localization landscape approach for classical waves at high frequencies using Webster's transformation.

Findings

Successfully applied the adapted landscape to classical wave systems

Predicted localized modes with high accuracy

Provided a computationally efficient tool for high-frequency localization analysis

Abstract

Anderson localization is a universal interference phenomenon occurring when a wave evolves through a random medium and it has been observed in a great variety of physical systems, either quantum or classical. The recently developed localization landscape theory offers a computationally affordable way to obtain useful information on the localized modes, such as their location or size. Here we examine this theory in the context of classical waves exhibiting high frequency localization and for which the original localization landscape approach is no longer informative. Using a Webster's transformation, we convert a classical wave equation into a Schr\"{o}dinger equation with the same localization properties. We then compute an adapted localization landscape to retrieve information on the original classical system. This work offers an affordable way to access key information on high-frequency mode localization.