On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line

Abstract

In this paper, we study spectral properties of a family of quasi-periodic Schrodinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curves are 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.

Cited by in corpus (3)

• Extended States for Polyharmonic Operators with Quasi-periodic Potentials in Dimension Two
• Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators
• Multiscale Analysis in Momentum Space for Quasi-periodic Potential in Dimension Two