On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current (Q2338947)

This paper deals with the study of various qualitative and asymptotic properties of the three-dimensional Laplace operator with a magnetic field created by an infinite rectilinear current bearing a constant current. The authors develop a precise asymptotic analysis of the band functions near the ground state energy. Next, in the case of a perturbed Hamiltonian by an electric potential, it is proved that for a slow decaying potential, infinitely many negative eigenvalues are created, whereas only a finite number of eigenvalues appears for a fast decaying potential. It is argued that the criterion about finiteness strongly depends on the decay rate of the potential with respect to the distance to the wire.