1 citations · 1 across the 17 of their papers we have counts for
4 papers · 2 filters
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…