On the Singular Spectrum for Adiabatic Quasiperiodic Schrodinger Operators

We study spectral properties of a family of quasiperiodic Schrodinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curve has a real branch that is extended along the momentum direction. In the energy intervals where this happens, we obtain an asymptotic formula for the Lyapunov exponent and show that the spectrum is purely singular. This result was conjectured and proved in a particular case by Fedotov and Klopp (2005).