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Spectral Asymptotics of a Singular Harmonic Oscillator with Aharonov--Bohm Flux
Bernard Helffer, Ayman Kachmar, François Nicoleau
Motivated by a recent article of R. Vanlaere (2026), we investigate the spectral asymptotics of a singular harmonic oscillator arising from the radial reduction of the magnetic Sch…
Bound states for the magnetic Neumann Laplacian in planar sectors
Ayman Kachmar, Mikael Sundqvist
We study the magnetic Neumann Laplacian in an infinite planar sector of opening under a constant magnetic field. Building on earlier work by Bonnaillie-Noël and collabo…
High Flux Asymptotics and Critical Phenomena for the Magnetic Laplacian
Emanuela L. Giacomelli, Ayman Kachmar, Mikael Sundqvist
We study the lowest eigenvalue of the Neumann magnetic Laplacian in a planar domain divided into two regions, with piecewise constant magnetic fields that may scale differently in…
Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk
Bernard Helffer, Ayman Kachmar, François Nicoleau
We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field li…
Quantum Tunneling and the Aharonov-Bohm effect
Bernard Helffer, Ayman Kachmar
We investigate a Hamiltonian with radial potential wells and an Aharonov-Bohm vector potential with two poles. Assuming that the potential wells are symmetric, we derive the semi-c…
The magnetic Laplacian on the Disc for strong magnetic fields
Ayman Kachmar, Germán Miranda
The magnetic Laplacian on a planar domain under a strong constant magnetic field has eigenvalues close to the Landau levels. We study the case when the domain is a disc and the spe…
Counting eigenvalues below the lowest Landau level
Soeren Fournais, Ayman Kachmar
For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary compo…
On the Laplace operator with a weak magnetic field in exterior domains
Ayman Kachmar, Vladimir Lotoreichik, Mikael Sundqvist
We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate…
A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function
Ayman Kachmar, Vladimir Lotoreichik
We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic field. This bound…