Singular continuous spectrum for a class of nonprimitive substitution Schrödinger operators

Abstract

We present a class of discrete Schrödinger operators, with potentials derived from nonprimitive substitutions, that has purely singular continuous spectrum. We give sufficient conditions on the substitution rule assuring singular continuous spectrum, either for a generic set in the hull of the potential or for a set of total invariant measure.

Locations

• Proceedings of the American Mathematical Society - View - PDF