Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
Year: 2026
Type: preprint
Abstract: We prove polynomial upper bounds on spectral gaps of quasi-periodic Schrödinger operators with small $C^{k}$ potentials and Diophantine frequencies. For sufficiently large $k$, the decay exponent is $k-34τ$, where $τ$ is the Diophantine exponent. We construct examples with lower bounds along infinitely many gap labels, showing that the leading coefficient $1$ of $k$ is asymptotically optimal. The proof uses quantitative reducibility and the Moser-Pöschel argument.
Source: arXiv (Cornell University)
Authors: Cai, Ao, Gao, Yang, He, Jiawei
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2246733594, 非解析位势薛定谔算子谱的行为及其应用
OpenAlex ID: W7223150475