Sharp arithmetic localization for quasiperiodic operators with monotone potentials

TL;DR

This paper establishes a universal sharp arithmetic localization property for a broad class of one-dimensional quasiperiodic Schrödinger operators with monotone potentials, advancing understanding of their spectral behavior.

Contribution

It proves the universality of sharp arithmetic localization for all such operators with anti-Lipschitz monotone potentials, a significant theoretical advancement.

Findings

Confirmed universality of localization across all considered operators

Extended localization results to a broader class of potentials

Provided new insights into spectral properties of quasiperiodic operators

Abstract

We prove the universality of sharp arithmetic localization for all one-dimensional quasiperiodic Schr\"odinger operators with anti-Lipschitz monotone potentials.