Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk
Abstract
We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field limit. This improves recent results of Helffer-Nicoleau (2025) based on special function asymptotics, and extends earlier works by Fournais-Helffer (2006), Kachmar (2006), and R. Fahs, L. Treust, N. Raymond, S. V\~u Ngoc (2024). Notably, our analysis reveals how the third term encodes the dependence on the magnetic flux. Finally, we investigate the weak magnetic field limit and establish the flux dependence in the asymptotics of Kachmar-Lotoreichik-Sundqvist (2025).
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.