Affiliations: Département de Mathématiques, Université Paris Sud, Bâtiment 425, 91405 Orsay Cedex, France | Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany
Note: [] Corresponding author: Konstantin Pankrashkin, Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany. Tel.: +49 30 2093 2352; Fax: +49 30 2093 2727; E-mail: const@mathematik.hu-berlin.de.
Abstract: The two-dimensional Schrödinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields and a weak coupling we reduce the spectral problem to the semiclassical analysis of one-dimensional Harper-like operators. This shows the existence of parts of Cantor structure in the spectrum for special values of the magnetic flux.
Keywords: Schrödinger operator, periodic perturbation, Cantor spectrum, magnetic field, zero-range potential
