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The Dirac bag model in strong magnetic fields

Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond and Edgardo Stockmeyer

Vol. 5 (2023), No. 3, 643–727
DOI: 10.2140/paa.2023.5.643
Abstract

We study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we establish the asymptotic behavior of the low-lying (positive and negative) energies in the limit of strong magnetic field. Moreover, for a constant magnetic field B, we study the problem on the half-plane and find that the Dirac operator has continuous spectrum except for a gap of size a0B, where a0 (0,2) is a universal constant. Remarkably, this constant characterizes certain energies of the system in a bounded domain as well. Our findings give a fairly complete description of the eigenvalue asymptotics of magnetic two-dimensional Dirac operators under general boundary conditions.

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Keywords
Dirac operator, magnetic fields, spectrum
Mathematical Subject Classification
Primary: 35Pxx, 81Qxx
Milestones
Received: 3 February 2022
Revised: 8 December 2022
Accepted: 2 February 2023
Published: 24 August 2023
Authors
Jean-Marie Barbaroux
Aix Marseille Univ
Université de Toulon
CNRS, CPT
Marseille
France
Loïc Le Treust
Aix Marseille Univ
CNRS
I2M
Marseille
France
Nicolas Raymond
Univ Angers
CNRS, LAREMA
Institut Universitaire de France, SFR MATHSTIC
F-49000 Angers
France
Edgardo Stockmeyer
Instituto de Física
Pontificia Universidad Católica de Chile
Santiago
Chile