Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors

Loïc Le Treust (1) , Thomas Ourmières-Bonafos (2)

1 I2M - Institut de Mathématiques de Marseille
2 LMO - Laboratoire de Mathématiques d'Orsay

This paper deals with the study of the two-dimensional Dirac operator with infinite mass boundary condition in a sector. We investigate the question of self-adjointness depending on the aperture of the sector: when the sector is convex it is self-adjoint on a usual Sobolev space whereas when the sector is non-convex it has a family of self-adjoint extensions parametrized by a complex number of the unit circle. As a byproduct of this analysis we are able to give self-adjointness results on polygones. We also discuss the question of distinguished self-adjoint extensions and study basic spectral properties of the operator in the sector.

Mots clés: Dirac operator; Spectral theory; Graphene; Corner domain; MIT bag model.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Loïc Le Treust, Thomas Ourmières-Bonafos. Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors. Annales Henri Poincaré, 2018, ⟨10.1007/s00023-018-0661-y⟩. ⟨hal-01561490v1⟩