Responsable : Geoffrey Powell
Magnetic fields varying on very short scales create an edge separating two uniform but distinct values of the magnetic field's intensity. What will be the energy levels of an electron moving in such a field ? Dependent on the geometry of the edge, we provide an answer to this question. The energy levels will be eigenvalues of a special magnetic Laplace operator involving the semiclassical parameter (a very small parameter compared to the sample’s scale). Based on a joint work with W. Assaad and B. Helffer, accurate eigenvalue asymptotics displaying the splitting between the consecutive eigenvalues can be derived through a variational proof not involving pseudo-differential calculus.