6 citations · 18 across the 15 of their papers we have counts for
7 papers · 1 filter
Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue
Bernard Helffer, Ayman Kachmar
We study the 3D Neuman magnetic Laplacian in the presence of a semi-classical parameter and a non-uniform magnetic field with constant intensity. We determine a sharp two term asym…
Semi-classical edge states for the Robin Laplacian
B. Helffer, A. Kachmar
Motivated by the study of high energy Steklov eigenfunctions, we examine the semi-classical Robin Laplacian. In the two dimensional situation, we determine an effective operator de…
Lowest energy band function for magnetic steps
Wafaa Assaad, Ayman Kachmar
We study the Schrödinger operator in the plane with a step magnetic field function. The bottom of its spectrum is described by the infimum of the lowest eigenvalue band function, f…
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…
Counterexample to strong diamagnetism for the magnetic Robin Laplacian
Ayman Kachmar, Mikael P. Sundqvist
We determine a counterexample to strong diamagnetism for the Laplace operator in the unit disc with a uniform magnetic field and Robin boundary condition. The example follows from…
Weyl formulae for the Robin Laplacian in the semiclassical limit
A Kachmar, P Keraval, N Raymond
This paper is devoted to establish semiclassical Weyl formulae for the Robin Laplacian on smooth domains in any dimension. Theirs proofs are reminiscent of the Born-Oppenheimer met…