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Arithmetic k-Polynomial Dynamical Localization for k Power-Law Quasi-Periodic Long-Range Operators on ℓ2(ℤd)

  • Ao Cai
  • Huihui Lv
  • Yuan Shan
  • Xueyin Wang
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Abstract

We establish a criterion of arithmetic k-polynomial spectral localization and k-polynomial dynamical localization in expectation for quasi-periodic long-range operators on ℓ2(ℤd) with power-law hopping based on the quantitative Ck-reducibility of the dual Schrödinger cocycle. As the application, we prove both localization properties for power-law long-range perturbations of the Almost Mathieu Operators with sufficiently large couplings and Diophantine frequencies.

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Cite

BibTeXRIS
BibTeX
@misc{cai2026arithmetic,
  title = {{Arithmetic $k$-Polynomial Dynamical Localization for $k$ Power-Law Quasi-Periodic Long-Range Operators on $\ell^2(\mathbbZ^d)$}},
  author = {Ao Cai and Huihui Lv and Yuan Shan and Xueyin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26012},
  eprint = {2609.26012},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26012},
}
RIS
TY  - UNPB
TI  - Arithmetic k-Polynomial Dynamical Localization for k Power-Law Quasi-Periodic Long-Range Operators on ℓ^2(ℤ^d)
AU  - Ao Cai
AU  - Huihui Lv
AU  - Yuan Shan
AU  - Xueyin Wang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26012
UR  - https://arxiv.org/abs/2609.26012
AB  - We establish a criterion of arithmetic k-polynomial spectral localization and k-polynomial dynamical localization in expectation for quasi-periodic long-range operators on ℓ^2(ℤ^d) with power-law hopping based on the quantitative C^k-reducibility of the dual Schrödinger cocycle. As the application, we prove both localization properties for power-law long-range perturbations of the Almost Mathieu Operators with sufficiently large couplings and Diophantine frequencies.
ER  -