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Journal of Spectral Theory

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Volume 7, Issue 3, 2017, pp. 847–879
DOI: 10.4171/JST/179

Published online: 2017-09-28

Spectral flow of exterior Landau–Robin hamiltonians

Magnus Goffeng[1] and Elmar Schrohe[2]

(1) Chalmers University of Technology, Göteborg, Sweden
(2) Leibniz Universität Hannover, Germany

We study the spectral ow of Landau–Robin hamiltonians in the exterior of a compact domain with smooth boundary. This provides a method to study the spectrum of the exterior Landau–Robin hamiltonian’s dependence on the choice of Robin data, even explaining the heuristics of how the spectrum of the Robin problem asymptotically tends to the spectrum of the Dirichlet problem. The main technical result concerns the continuous dependence of Landau–Robin hamiltonians on the Robin data in the gap topology. The problem can be localized to the compact boundary where the asymptotic behavior of the spectral ow in some special cases can be described.

Keywords: Spectral flow, magnetic Schrödinger operator, boundary value problem, exterior problem

Goffeng Magnus, Schrohe Elmar: Spectral flow of exterior Landau–Robin hamiltonians. J. Spectr. Theory 7 (2017), 847-879. doi: 10.4171/JST/179