On gaps in the spectra of quasiperiodic Schr\"odinger operators with
discontinuous monotone potentials
On gaps in the spectra of quasiperiodic Schr\"odinger operators with
discontinuous monotone potentials
We show that, for one-dimensional discrete Schr\"odinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectra. The argument is based on well-known result of Gordon and Simon, combined with a way to consider perturbations whose ranges are not necessarily cyclic. The …