Counting function of magnetic resonances for exterior problems

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 ${\mathbb{R}}^3$ of the 3D Schr{ö}dinger operator with constant magnetic field of scalar intensity $b\textgreater{}0$. 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.

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• Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
• Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains
• Magnetic edge states
• On mathematical models for Bose-Einstein condensates in optical lattices (expanded version)
• Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian
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Cited by in corpus (1)

• Threshold singularities of the spectral shift function for geometric perturbations of magnetic Hamiltonians