COUNTING FUNCTION OF MAGNETIC RESONANCES FOR EXTERIOR PROBLEMS
Language
en
Document de travail - Pré-publication
English Abstract
We study the asymptotic distribution of the resonances near the Landau levels $\Lambda_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of ...Read more >
We study the asymptotic distribution of the resonances near the Landau levels $\Lambda_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of $\mathbb{R}^3$ of the 3D Schrödinger operator with constant magnetic field of scalar intensity $b>0$. We investigate the corresponding resonance counting function and obtain the main asymptotic term. In particular, we prove the accumulation of resonances at the Landau levels and the existence of resonance free sectors. In some cases, it provides the discreteness of the set of embedded eigenvalues near the Landau levels.Read less <
ANR Project
Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution - ANR-11-BS01-0019
Origin
Hal imported