56 citations · 305 across the 37 of their papers we have counts for
49 papers
Boundary states of the Robin magnetic Laplacian
Rayan Fahs, Loïc Le Treust, Nicolas Raymond +1
This article tackles the spectral analysis of the Robin Laplacian on a smooth bounded two-dimensional domain in the presence of a constant magnetic field. In the semiclassical limi…
Purely magnetic tunnelling between radial magnetic wells
Søren Fournais, Léo Morin, Nicolas Raymond
This article is devoted to the semiclassical spectral analysis of the magnetic Laplacian in two dimensions. Assuming that the magnetic field is positive and has two symmetric radia…
Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions
Khaled Abou Alfa, Maha Aafarani, Frédéric Hérau +1
This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the vari…
Correlative mapping of local hysteresis properties in VO
Melissa Alzate Banguero, Sayan Basak, Nicolas Raymond +6
We have developed a new optical microscopy technique able to track micron-sized surface clusters as temperature is varied. Potential candidates for study include phase separated me…
Discrete spectrum of the magnetic Laplacian on perturbed half-planes
Virginie Bonnaillie-Noël, Søren Fournais, Ayman Kachmar +1
The existence of bound states for the magnetic Laplacian in unbounded domains can be quite challenging in the case of a homogeneous magnetic field. We provide an affirmative answer…
Effective operators on an attractive magnetic edge
Soeren Fournais, Bernard Helffer, Ayman Kachmar +1
The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontin…
On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields
Enguerrand Bon-Lavigne, Loïc Le Treust, Nicolas Raymond +1
We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum…
Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field
Frédéric Hérau, Nicolas Raymond
This article deals with the spectral analysis of the semiclassical Neumann magnetic Laplacian on a smooth bounded domain in dimension three. When the magnetic field is constant and…
Magnetic quantum currents in the presence of a Neumann wall
Nicolas Raymond, Éric Soccorsi
We consider the Schrödinger operator with constant transverse magnetic field on a half-plane, endowed with Neumann boundary conditions. We study the low energy currents flowing alo…
Eigenvalue asymptotics for confining magnetic Schrödinger operators with complex potentials
Léo Morin, Nicolas Raymond, San Vu Ngoc
This article is devoted to the spectral analysis of the electro-magnetic Schrödinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential ef…
On the two-dimensional quantum confined Stark effect in strong electric fields
Horia Cornean, David Krejcirik, Thomas Garm Pedersen +2
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity…
On the Dirac bag model in strong magnetic fields
Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond +1
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 call…
Magnetic confinement for the 3D Robin Laplacian
Bernard Helffer, Ayman Kachmar, Nicolas Raymond
We determine accurate asymptotics of the lowest eigenvalue for the Laplace operator with a smooth magnetic field and Robin boundary conditions in a smooth 3D domain, when the Robin…
Magnetic WKB constructions on surfaces
Yannick Guedes Bonthonneau, Tho Nguyen Duc, Nicolas Raymond +1
This article is devoted to the description of the eigenvalues and eigenfunctions of the magnetic Laplacian in the semiclassical limit via the complex WKB method. Under the assumpti…
Purely magnetic tunneling effect in two dimensions
Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond
The semiclassical magnetic Neumann Schrödinger operator on a smooth, bounded, and simply connected domain of the Euclidean plane is considered. When has a symmetry axis, th…
Exponential localization in 2D pure magnetic wells
Yannick Guedes Bonthonneau, Nicolas Raymond, San Vũ Ngoc
We establish a magnetic Agmon estimate in the case of a purely magnetic single non-degenerate well, by means of the Fourier-Bros-Iagolnitzer transform and microlocal exponential es…
Absence of embedded eigenvalues for translationally invariant magnetic Laplacians
Nicolas Raymond, Julien Royer
Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum und…
On the semiclassical spectrum of the Dirichlet-Pauli operator
Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond +1
This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magne…
The MIT Bag Model as an infinite mass limit
Naiara Arrizabalaga, Loïc Le Treust, Albert Mas +1
The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass lies outside a smooth and bounded open set , it is proved that its spe…
On the semiclassical Laplacian with magnetic field having self-intersecting zero set
Monique Dauge, Jean-Philippe Miqueu, Nicolas Raymond
This paper is devoted to the spectral analysis of the Neumann realization of the 2D magnetic Laplacian with semiclassical parameter h > 0 in the case when the magnetic field vanish…
Boundary effects on the magnetic Hamiltonian dynamics in two dimensions
Tho Nguyen Duc, Nicolas Raymond, San Vu Ngoc
We study the Hamiltonian dynamics of a charged particle submitted to a pure magnetic field in a two-dimensional domain. We provide conditions on the magnetic field in a neighbourho…
On the stability of the Schwartz class under the magnetic Schrödinger flow
Grégory Boil, Nicolas Raymond, San Vu Ngoc
We prove that the Schwartz class is stable under the magnetic Schrödinger flow when the magnetic -form is non-degenerate and does not oscillate too much at infinity.
WKB constructions in bidimensional magnetic wells
Yannick Bonthonneau, Nicolas Raymond
This article establishes, in an analytic framework and in two dimensions, the first WKB constructions describing the eigenfunctions of the pure magnetic Laplacian with low energy w…
Reduction of dimension as a consequence of norm-resolvent convergence and applications
David Krejcirik, Nicolas Raymond, Julien Royer +1
This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The effic…