Perturbative diagonalisation for Maryland-type quasiperiodic operators with flat pieces

TL;DR

This paper proves Anderson localization for a class of quasiperiodic operators with flat segments in their sampling functions, under certain geometric conditions and at high disorder levels.

Contribution

It extends localization results to Maryland-type operators with non-strictly monotone and flat sampling functions, under specific geometric assumptions.

Findings

Localization holds at large disorder levels.

Operators with flat segments can exhibit Anderson localization.

Geometric conditions are crucial for localization results.

Abstract

We consider quasiperiodic operators on $\mathbb Z^d$ with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on the frequencies, lengths of the segments, and their positions, we show that these operators enjoy Anderson localization at large disorder.