Coexistence of ac and pp spectrum for kicked quasi-periodic potentials

Abstract

We introduce a class of real analytic "peaky" potentials for which the corresponding quasi-periodic 1D Schrödinger operators exhibit, for quasiperiodic frequencies in a set of positive Lebesgue measure, both absolutely continuous and pure point spectrum.

35 pages, 3 figures

References in corpus (2)

• The absolutely continuous spectrum of the almost Mathieu operator
• A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies

Cited by in corpus (1)

• Exact mobility edges for 1D quasiperiodic models