On the spectrum of an "even" periodic Schrödinger operator with a rational magnetic flux

  • Nikolai D. Filonov

    Steklov Mathematical Institute, St. Petersburg, Russian Federation
  • Alexander V. Sobolev

    University College London, UK

Abstract

We study the Schrödinger operator on L2(R3)L_2(\mathbb R^3) 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.

Cite this article

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. 381–398

DOI 10.4171/JST/102