From the 1 of 13 linked papers with an AI index.
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Bound states for the magnetic Neumann Laplacian in planar sectors
Ayman Kachmar, Mikael Sundqvist
The paper proves that a magnetic Neumann Laplacian on any convex planar sector under a constant magnetic field has a discrete ground‑state eigenvalue, showing the spectrum’s bottom…
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…