Browsing by Author "Gohlke, Philipp"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Zero measure spectrum for multi-frequency Schrödinger operators
    (EMS Press, 2022) Chaika, Jon; Damanik, David; Fillman, Jake; Gohlke, Philipp
    Building on works of Berthé–Steiner–Thuswaldner and Fogg–Nous, we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence, we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrödinger operator has Cantor spectrum of zero Lebesgue measure. We also describe a framework that can allow this to be extended to higher-dimensional tori.