6 papers
Dirac bag model on thin domains: a microlocal viewpoint
Loïc Le Treust, Thomas Ourmières-Bonafos, Nicolas Raymond
The Dirac operator is considered on a bidimensional domain whose boundary carries the infinite mass boundary condition. The analysis is focused on the existence of discrete spectru…
Two-dimensional Dirac operators with singular interactions supported on closed curves
Jussi Behrndt, Markus Holzmann, Thomas Ourmières-Bonafos +1
We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar -interactions of constant strengths supported on a smooth closed cu…
Dirac operators and shell interactions: a survey
Thomas Ourmières-Bonafos, Fabio Pizzichillo
In this survey we gather recent results on Dirac operators coupled with -shell interactions. We start by discussing recent advances regarding the question of self-adjointness fo…
A sharp upper bound on the spectral gap for graphene quantum dots
Vladimir Lotoreichik, Thomas Ourmières-Bonafos
The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected -domains with infinite mass bounda…
Dirac operators on hypersurfaces as large mass limits
Andrei Moroianu, Thomas Ourmières-Bonafos, Konstantin Pankrashkin
We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either…
Effective operators for Robin eigenvalues in domains with corners
Magda Khalile, Thomas Ourmières-Bonafos, Konstantin Pankrashkin
We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of severa…