Mathematics

This talk will concern the spectral analysis of the Schrödinger operator with external magnetic field and a semi-classical parameter h, on a bounded and regular domain D in two dimensions, with Neumann boundary condition. We will investigate the case when the magnetic field vanishes along a union of smooth curves. The aim is to understand the influence of the cancellations and to present the behaviour of the lowest eigenvalues and the associated eigenfunctions when h vanishes (semi-classical limit). Numerical simulations based on the finite elements library Mélina++ have guided the analysis and illustrate the obtained results.