2017/11/23 by Wenwen Jian, Yunfeng Shi, Jian, Wenwen +3
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.1711.08661
openalex publication_date 2017/11/23 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28
In this paper, we study the quasi-periodic operators Hε,ω(x): (Hε,ω(x)ψ)n=ε∑k∈ℤWkψn-k+V(x+nω)ψn, where ψ=\ψn\∈ℓ2(ℤ,ℂl), V(x)=diag(v1(x),⋯,vl(x)) with vi (1≤ i ≤ l) being real analytic functions on \mathbbT=ℝ/ℤ and Wk (k∈ℤ) being l× l matrices satisfying ‖Wk‖≤ C0e-ρ|k|. Using techniques developed by Bourgain and Goldstein [Ann. of Math. 152(3):835--879, 2000], we show that for |ε|≤ ε0(V,ρ,l,C0) ( depending only on V,ρ, l, C0) and x∈ ℝ/ℤ, there is some full Lebesgue measure subset F of the Diophantine frequencies such that Hε,ω(x) exhibits Anderson localization if ω∈ F.