Abstract
Consider Γ, a non-degenerate lattice in \({{\mathbb R}^2}\) and a constant magnetic field B with a flux though a cell of Γ that is a rational multiple of 2π. We prove that for a generic Γ-periodic potential V, the spectrum of the Landau Hamiltonian with magnetic field B and periodic potential V is purely absolutely continuous.
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Part of this work was done during the conference “Spectral analysis of differential operators” held at the MFO, Oberwolfach (29/11–03/12/2004); it is a pleasure to thank T. Weidl and A. Sobolev, the organizers of the conference, for their invitation to participate to the meeting as well as D. Elton for stimulating discussions. It is also a pleasure to thank the Institute of Mathematics of Hanoi, where this work was completed, for its kind hospitality.
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Klopp, F. Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential. Math. Ann. 347, 675–687 (2010). https://doi.org/10.1007/s00208-009-0452-3
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DOI: https://doi.org/10.1007/s00208-009-0452-3