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arXiv · 2610.17139

(Sharp arithmetic) localization beyond transversality

Svetlana Jitomirskaya·Netanel Levi·Tom Stoiber
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Abstract

We prove sharp arithmetic localization for one-dimensional quasiperiodic potentials with jump discontinuities, beyond uniform transversality. Our results include every non-constant $C^1$ monotone sampling function, even with arbitrarily large flat regions, and also certain non-monotone potentials. A key new mechanism is a symbolic unique-continuation principle: first-return words to the region where $f'>0$ have no common Dirichlet resonance, forcing eigenfunction mass to transfer away from flat or negatively sloped regions and recovering quantitative monotonicity of finite-volume eigenvalue branches.

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Svetlana Jitomirskaya, Netanel Levi, Tom Stoiber. 2026-10-12. (Sharp arithmetic) localization beyond transversality. https://arxiv.org/abs/2610.17139

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