14 citations · 118 across the 45 of their papers we have counts for
53 papers
Counting Negative Eigenvalues for the Magnetic Pauli Operator
Søren Fournais, Rupert L. Frank, Magnus Goffeng +2
We study the Pauli operator in a two-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues remi…
Flux and symmetry effects on quantum tunneling
Bernard Helffer, Ayman Kachmar, Mikael Persson Sundqvist
Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitia…
Discrete spectrum of the magnetic Laplacian on perturbed half-planes
Virginie Bonnaillie-Noël, Søren Fournais, Ayman Kachmar +1
The existence of bound states for the magnetic Laplacian in unbounded domains can be quite challenging in the case of a homogeneous magnetic field. We provide an affirmative answer…
Quantum tunneling in deep potential wells and strong magnetic field revisited
B. Helffer, A. Kachmar
Inspired by a recent paper by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic…
Effective operators on an attractive magnetic edge
Soeren Fournais, Bernard Helffer, Ayman Kachmar +1
The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontin…
Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue
Bernard Helffer, Ayman Kachmar
We study the 3D Neuman magnetic Laplacian in the presence of a semi-classical parameter and a non-uniform magnetic field with constant intensity. We determine a sharp two term asym…