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Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
Abstract
We prove polynomial upper bounds on spectral gaps of quasi-periodic Schrödinger operators with small Ck 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.
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BibTeX
@misc{cai2026polynomial,
title = {{Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators}},
author = {Ao Cai and Yang Gao and Jiawei He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26977},
eprint = {2610.26977},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26977},
}
RIS
TY - UNPB
TI - Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
AU - Ao Cai
AU - Yang Gao
AU - Jiawei He
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26977
UR - https://arxiv.org/abs/2610.26977
AB - 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.
ER -