We study the Schrödinger operator on with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the (appropriately defined) flux of the magnetic field is rational. Under these assumptions it is shown that the spectrum of the operator is absolutely continuous. Previously known results on absolute continuity for periodic operators were obtained for the zero magnetic flux.
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Nikolai D. Filonov, Alexander V. Sobolev, On the spectrum of an "even" periodic Schrödinger operator with a rational magnetic flux. J. Spectr. Theory 5 (2015), no. 2, pp. 381–398DOI 10.4171/JST/102