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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

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