Crossover Between Quantum and Classical Waves and High Frequency Localization Landscapes

• Main Authors: Colas, David, Bellis, Cédric, Lombard, Bruno, Cottereau, Régis
• Format: Journal Article
• Language: English
• Published: 25-04-2022
• Subjects: Physics - Classical Physics; Physics - Disordered Systems and Neural Networks; Physics - Quantum Gases
• DOI: 10.48550/arxiv.2204.11632

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.