2020/03/31 by Lingrui Ge, Ge, Lingrui, Jiangong You +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2003.13946
openalex publication_date 2020/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya \citeJ for the almost Mathieu operators (AMO). Later, the result was generalized by Bourgain and Jitomirskaya \citebj02 to a class of \it one dimensional quasi-periodic long-range operators. In this paper, we propose a novel approach based on an arithmetic version of Aubry duality and quantitative reducibility. Our method enables us to prove the same result for the class of quasi-periodic long-range operators in \it all dimensions, which includes \citeJ, bj02 as special cases.