Purely magnetic tunnelling between radial magnetic wells

2023/08/08 by Søren Fournais, Fournais, Søren, Léo Morin +3 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2308.04315

openalex publication_date 2023/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is devoted to the semiclassical spectral analysis of the magnetic Laplacian in two dimensions. Assuming that the magnetic field is positive and has two symmetric radial wells, we establish an accurate tunnelling formula, that is a one-term estimate of the spectral gap between the lowest two eigenvalues. This gap is exponentially small when the semiclassical parameter goes to zero, but positive.

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