Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime

Abstract

We study the spectral transition line of the extended Harper's model in the positive Lyapunov exponent regime. We show that both pure point spectrum and purely singular continuous spectrum occur for dense subsets of frequencies on the transition line.

18 pages

References in corpus (2)

• Full measure reducibility and localization for Jacobi operators: a topological criterion
• Universal hierarchical structure of quasiperiodic eigenfunctions