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Journal Articles Pure and Applied Analysis Year : 2023

On the Dirac bag model in strong magnetic fields


In this work 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 $a_0\sqrt{B}$, where $a_0\in (0,\sqrt{2})$ is a universal constant. Remarkably, this constant characterizes certain energies of the system in a bounded domain as well. We discuss how these findings, together with our previous work, give a fairly complete description of the eigenvalue asymptotics of magnetic two-dimensional Dirac operators under general boundary conditions.
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Dates and versions

hal-02889558 , version 1 (06-07-2020)
hal-02889558 , version 2 (13-11-2020)
hal-02889558 , version 3 (30-04-2021)



Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond, Edgardo Stockmeyer. On the Dirac bag model in strong magnetic fields. Pure and Applied Analysis, inPress, 5 (3), pp.643-727. ⟨10.2140/paa.2023.5.643⟩. ⟨hal-02889558v3⟩
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