1. On the Dirac bag model in strong magnetic fields
- Author
-
Barbaroux, Jean-Marie, Treust, Loïc Le, Raymond, Nicolas, Stockmeyer, Edgardo, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), CPT - E8 Dynamique quantique et analyse spectrale, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Pontificia Universidad Católica de Chile (UC), ANR-17-CE40-0016,DYRAQ,Dynamique des systèmes quantiques relativistes(2017), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
- Subjects
Mathematics - Analysis of PDEs ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,FOS: Mathematics ,FOS: Physical sciences ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Mathematical Physics (math-ph) ,Mathematical Physics ,Analysis of PDEs (math.AP) - Abstract
International audience; 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.