Abstract
Let H0 = (i∇ – A)2 be the Schrodinger operator with constant magnetic field in Rd, d = 2,3 and K ⊂ Rd be a compact domain with smooth boundary.We consider the Dirichlet (resp. Neumann, resp. Robin) realization of (i∇–A)2 on Ω := Rd K. First, in the case d = 2, we recall the known results concerning eigenvalue clusters for these exterior problems. Then, in dimension 3, after a review on the previous results for potential perturbations, we study the resonances for the obstacle problems. We establish the existence of resonance free sectors near the Landau level and study a resonance counting function. Consequently we obtain the accumulation of resonances at the Landau levels and in some cases the discretness of the set of the embedded eigenvalues.
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