Localization for quasiperiodic operators with unbounded monotone potentials

TL;DR

This paper proves non-perturbative Anderson localization for a broad class of 1D quasiperiodic operators with unbounded monotone potentials, extending classical and perturbative results to more general settings.

Contribution

It introduces a non-perturbative approach to establish localization for unbounded monotone potentials in 1D quasiperiodic operators, broadening the scope beyond analytic cases.

Findings

Proves Anderson localization for unbounded monotone potentials.

Extends classical results from the Maryland model.

Generalizes perturbative results to non-analytic potentials.

Abstract

We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland model and perturbative results for analytic potentials by B\'ellissard, Lima, and Scoppola.