Localized Eigenfunctions: Here You See Them, There You Don't

TL;DR

This paper investigates the phenomenon of eigenfunction localization for the Laplacian on compact domains, focusing on a specific numerically identified low-frequency localized eigenfunction.

Contribution

It provides an in-depth analysis of eigenfunction localization, highlighting a particular example of a localized low-frequency eigenfunction in a compact domain.

Findings

Identification of a numerically localized low-frequency eigenfunction

Insights into the conditions leading to eigenfunction localization

Potential implications for spectral geometry and physics

Abstract

This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.