Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: University of California, Berkeley
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221746313