%0 Journal Article
%T On the lowest energy of a 3D magnetic hamiltonian with axisymmetric potential
%A Nicolas Popoff
%J Mathematics
%D 2013
%I arXiv
%X We study the bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the "de Gennes" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3.
%U http://arxiv.org/abs/1309.6080v1