Absolutely continuous spectrum for magnetic Schrödinger operators

In 1973 L. Thomas proved that the periodic Schrödinger operator in Euclidean space has absolutely continuous spectrum. It was only 25 years later that the first non-trivial generalizations were found (for Schrödinger operators with zero flux magnetic field), and there has been quite some progress recently.

We will review the basic principles of the method and the typical problems which arise. We will also investigate the case when the magnetic flux is not zero.