6 papers
Monotonicity and the de Gennes bound for the magnetic Neumann Laplacian in the disk
Corentin Léna, Mikael Sundqvist
We consider the lowest eigenvalue of the magnetic Neumann Laplacian in the unit disk, for a constant magnetic field of strength . We prove that is strictly increasi…
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…
A magnetic eigenvalue bound in the disk
Corentin Léna, Mikael Sundqvist
We consider the magnetic Schrödinger operator in the unit disk with constant magnetic field of strength and magnetic Neumann boundary condition. If denotes its lowes…
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…