Full measure reducibility and localization for Jacobi operators: a topological criterion

TL;DR

This paper establishes a topological criterion linking reducibility to constant rotations with dual localization in analytic quasiperiodic Jacobi operators, revealing a sharp phase transition in the extended Harper's model.

Contribution

It introduces a novel topological criterion connecting reducibility and localization, and applies it to identify a precise phase transition in the extended Harper's model.

Findings

Established a topological criterion for reducibility and localization.

Identified the sharp arithmetic phase transition in the extended Harper's model.

Connected spectral properties with topological and arithmetic conditions.

Abstract

We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase transition for the extended Harper's model in the positive Lyapunov exponent region.