2020/09/24 by Jon Chaika, Chaika, Jon, David Damanik +5
Mathematics · Physics and Astronomy · #Absolute continuity #Computer science #Discrete mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometry #Lebesgue integration #Lebesgue measure #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Measure (data warehouse) #Null set #Operator (biology) #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #Topological Materials and Phenomena #Torus #Translation (biology) #Zero (linguistics) #math-ph #math.DS #math.MP #math.SP
paper · pdf · doi:10.48550/arxiv.2009.11946
published in arXiv (Cornell University) (Cornell University) · 17 pages
arxiv created 2020/09/24 · openalex publication_date 2020/09/24 · arxiv updated 2020/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.