Quasiballistic Transport for Discrete One-Dimensional Quasiperidic Schrödinger Operators

2024/07/19 by Lian Haeming, Haeming, Lian
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.14228

openalex publication_date 2024/07/19 · openalex created_date 2024/09/26 · openalex updated_date 2026/07/28

Abstract

We obtain (up to logarithmic scaling) the power-law lower bound M_p(T_k)\gtrsim T_k^(1-δ)p on a subsequence T_k→∞, uniformly across p>0, for discrete one-dimensional quasiperiodic Schrödinger operators with frequencies satisfying β(α)>\frac3δmin_σγ. We achieve this by obtaining a quantitative ballistic lower bound for the Abel-averaged time evolution of general periodic Schrödinger operators in terms of the bandwidths. A similar result without uniformity, which assumes β(α)>\fracCδmin_σγ, was obtained earlier by Jitomirskaya and Zhang, for an implicit constant C<∞.

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