1 citations · 1 across the 17 of their papers we have counts for
17 papers
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…
Semiclassical resonances under local magnetic fields
Pavel Exner, Ayman Kachmar
We study resonances for the semiclassical magnetic Laplacian in the full plane with a compactly supported magnetic field in the framework of semiclassical complex scaling and black…
Isoperimetric inequalities for the lowest magnetic Steklov eigenvalue
Ayman Kachmar, Vladimir Lotoreichik
This paper studies the optimization of the lowest eigenvalue of the magnetic Steklov problem on planar domains. In the bounded domain setting and for magnetic fields of moderate st…
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…
Existence of Bulk Vortices in Superconductors with Strong Magnetic Fields
M. Correggi, A. Kachmar
We study the vortex formation in extreme type-II superconductors immersed in strong magnetic fields in the framework of the the Ginzburg-Landau theory. We focus on the regime where…
Isoperimetric inequality with zero magnetic field in doubly connected domains
Mrityunjoy Ghosh, Ayman Kachmar
We investigate how the lowest eigenvalue of a magnetic Laplacian depends on the geometry of a planar domain with a disk shaped hole, where the magnetic field is generated by a sing…
Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
Bernard Helffer, Ayman Kachmar, Francois Nicoleau
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operato…
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…
Local strong magnetic fields and the Little-Parks effect
Ayman Kachmar, Mikael Sundqvist
Starting from the Ginzburg--Landau model in a planar simply connected domain, with a local compactly supported applied magnetic field, we derive an effective model in the strong fi…
On the Ginzburg-Landau Energy of Corners
Michele Correggi, Emanuela L. Giacomelli, Ayman Kachmar
It is a well known fact that the geometry of a superconducting sample influences the distribution of the surface superconductivity for strong applied magnetic fields. For instance,…
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…
Isoperimetric inequalities for inner parallel curves
Charlotte Dietze, Ayman Kachmar, Vladimir Lotoreichik
We prove weighted isoperimetric inequalities for smooth, bounded, and simply connected domains. More precisely, we show that the moment of inertia of inner parallel curves for doma…