Eigenvalues of the Neumann magnetic Laplacian in the unit disk

2024/11/18 by Bernard Helffer, Helffer, Bernard, Corentin Léna +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2411.11721

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the first eigenvalue of the magnetic Laplacian with Neumann boundary conditions in the unit disk \mathbb D in \mathbb R². There is a rather complete asymptotic analysis when the constant magnetic field tends to +∞ and some inequalities seem to hold for any value of this magnetic field, leading to rather simple conjectures. Our goal is to explore these questions by revisiting a classical picture of the physicist D. Saint-James theoretically and numerically. On the way, we revisit the asymptotic analysis in light of the asymptotics obtained by Fournais-Helffer, that we can improve by combining them with a formula stated by Saint-James.

Cited by

• Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk
• Three-dimensional magnetic Schrödinger operator with the potential supported in a tube

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