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Semiclassical eigenvalue estimates under magnetic steps

Wafaa Assaad, Bernard Helffer and Ayman Kachmar

Vol. 17 (2024), No. 2, 535–585
Abstract

We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues for the Dirichlet magnetic Laplacian with a nonuniform magnetic field having a jump discontinuity along a smooth curve. The asymptotics hold in the semiclassical limit, which also corresponds to a large magnetic field limit and is valid under a geometric assumption on the curvature of the discontinuity curve.

Keywords
semiclassical analysis, magnetic Laplacian, magnetic steps
Mathematical Subject Classification
Primary: 35P15, 35P20, 81Q20
Milestones
Received: 6 September 2021
Revised: 25 March 2022
Accepted: 11 July 2022
Published: 6 March 2024
Authors
Wafaa Assaad
Faculty of Arts and Sciences
Lebanese International University
Beirut
Lebanon
Bernard Helffer
Laboratoire de Mathématiques Jean Leray
Université de Nantes
Nantes
France
Ayman Kachmar
School of Science and Engineering
The Chinese University of Hong Kong (Shenzhen)
Shenzhen
China

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