39 citations · 217 across the 17 of their papers we have counts for
20 papers
Geometric spectral properties of electromagnetic waveguides
Philippe Briet, Maxence Cassier, Thomas Ourmières-Bonafos +1
Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide…
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…
Spectral asymptotics of the Dirac operator in a thin shell
Vladimir Lotoreichik, Thomas Ourmières-Bonafos
We investigate the spectrum of the Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a smooth compact hypersurface in without…
Spectral asymptotics for two-dimensional Dirac operators in thin waveguides
William Borrelli, Nour Kerraoui, Thomas Ourmières-Bonafos
We consider the two-dimensional Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a -planar curve. Under generic assumptions on its curv…
Spectral properties of relativistic quantum waveguides
William Borrelli, Philippe Briet, David Krejcirik +1
We make a spectral analysis of the massive Dirac operator in a tubular neighborhood of an unbounded planar curve,subject to infinite mass boundary conditions. Under general assumpt…
A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities
Pedro R. S. Antunes, Rafael D. Benguria, Vladimir Lotoreichik +1
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of . Motivated by spectral geometric inequali…
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…
Dirac operators with Lorentz scalar shell interactions
Markus Holzmann, Thomas Ourmières-Bonafos, Konstantin Pankrashkin
This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of…
Dirichlet spectrum of the Fichera layer
Monique Dauge, Yvon Lafranche, Thomas Ourmières-Bonafos
We investigate the spectrum of the three-dimensional Dirichlet Laplacian in a prototypal infinite polyhedral layer, that is formed by three perpendicular quarter-plane walls of con…
Spectral asymptotics for -interactions on sharp cones
Thomas Ourmières-Bonafos, Konstantin Pankrashkin, Fabio Pizzichillo
We investigate the spectrum of three-dimensional Schrödinger operators with -interactions of constant strength supported on circular cones. As shown in earlier works, such opera…
Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors
Loïc Le Treust, Thomas Ourmières-Bonafos
This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on…
A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions
Thomas Ourmières-Bonafos, Luis Vega
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a -compact surface without boundary. To do so we are…
Discrete spectrum of interactions concentrated near conical surfaces
Thomas Ourmières-Bonafos, Konstantin Pankrashkin
We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schrödinger operators with attractive -interactions s…
Spectral transitions for Aharonov-Bohm Laplacians on conical layers
David Krejcirik, Vladimir Lotoreichik, Thomas Ourmières-Bonafos
We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dir…
On the Bound States of Schrödinger Operators with -interactions on Conical Surfaces
Vladimir Lotoreichik, Thomas Ourmières-Bonafos
In dimension greater than or equal to three, we investigate the spectrum of a Schr{ö}dinger operator with a -interaction supported on a cone whose cross section is the sphere of…
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
Monique Dauge, Thomas Ourmières-Bonafos, Nicolas Raymond
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture l…