We study a two-dimensional Pauli operator describing a charged quantum particle with spin
1= 2 moving on a plane in presence of an orthogonal Aharonov–Bohm magnetic flux. We …

We consider two-dimensional unbounded magnetic Dirac operators, either defined on the
whole plane or with infinite mass boundary conditions on a half-plane. Our main results use …

We consider the magnetic Dirichlet Laplacian with constant magnetic field on domains of
finite measure. First, in the case of a disk, we prove that the eigenvalue branches with …

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 …

We study Dirac operators on two-dimensional domains coupled to a magnetic field
perpendicular to the plane. We focus on the infinite-mass boundary condition (also called …

In 1996 Erdős showed that among planar domains of fixed area, the smallest principal
eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on …

We study the small singular values of the 2-dimensional semiclassical differential operator
P= 2 e-ϕ/h∘ h D z¯∘ e ϕ/h on S 1+ i S 1 and on S 1+ i R, where ϕ is given by sin y and by y …

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 …

We consider a Dirac operator with constant magnetic field defined on a half-plane with
boundary conditions that interpolate between infinite mass and zigzag. By a detailed study …

In this paper, we study the localization and propagation properties of the edge states
associated with a class of magnetic Laplacians in R 2. We assume that the intensity of the …