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Arithmetic localization for quasiperiodic long-range operators with monotone potentials

  • Hongyi Cao
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Abstract

We study one-dimensional quasiperiodic operators with α-Hölder monotone potentials and long-range hopping satisfying |T(x,y)|≤ ε e−ρ|x−y|. Under an explicit smallness condition on ε, we establish uniform Anderson localization for such operators in the regime ρ>αβ, where β is the exponential strength of frequency resonances. Our proof extends the arithmetic localization strategy for monotone quasiperiodic Schrödinger operators by Jitomirskaya and Kachkovskiy to the long-range setting, without relying on the Lyapunov exponent.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026arithmetic,
  title = {{Arithmetic localization for quasiperiodic long-range operators with monotone potentials}},
  author = {Hongyi Cao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39448},
  eprint = {2610.39448},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39448},
}
RIS
TY  - UNPB
TI  - Arithmetic localization for quasiperiodic long-range operators with monotone potentials
AU  - Hongyi Cao
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39448
UR  - https://arxiv.org/abs/2610.39448
AB  - We study one-dimensional quasiperiodic operators with α-Hölder monotone potentials and long-range hopping satisfying |T(x,y)|≤ ε e^−ρ|x−y|. Under an explicit smallness condition on ε, we establish uniform Anderson localization for such operators in the regime ρ>αβ, where β is the exponential strength of frequency resonances. Our proof extends the arithmetic localization strategy for monotone quasiperiodic Schrödinger operators by Jitomirskaya and Kachkovskiy to the long-range setting, without relying on the Lyapunov exponent.
ER  -