14 citations · 24 across the 5 of their papers we have counts for
7 papers
A 3D-Schroedinger operator under magnetic steps with semiclassical applications
Wafaa Assaad, Emanuela L. Giacomelli
We define a Schrödinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in th…
Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)
Wafaa Assaad, Bernard Helffer, Ayman Kachmar
We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a…
Lowest energy band function for magnetic steps
Wafaa Assaad, Ayman Kachmar
We study the Schrödinger operator in the plane with a step magnetic field function. The bottom of its spectrum is described by the infimum of the lowest eigenvalue band function, f…
Magnetic steps on the threshold of the normal state
Wafaa Assaad
Superconductivity in the presence of a step magnetic field has been recently the focus of many works. This contribution examines the behavior of a two-dimensional superconducting d…
The breakdown of superconductivity in the presence of magnetic steps
Wafaa Assaad
Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the pr…
The distribution of superconductivity near a magnetic barrier
Wafaa Assaad, Ayman Kachmar, Mikael Persson-Sundqvist
We consider the Ginzburg-Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise…