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On the Dirac bag model in strong magnetic fields

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02889558
Contributor : Loïc Le Treust Connect in order to contact the contributor
Submitted on : Friday, April 30, 2021 - 2:12:28 PM
Last modification on : Friday, January 7, 2022 - 9:34:03 AM

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  • HAL Id : hal-02889558, version 3
  • ARXIV : 2007.03242

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Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond, Edgardo Stockmeyer. On the Dirac bag model in strong magnetic fields. 2021. ⟨hal-02889558v3⟩

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