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

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.

Referee comments incorporated

References in corpus (7)

• Sharp Phase transitions for the almost Mathieu operator
• The absolutely continuous spectrum of the almost Mathieu operator
• Almost reducibility and absolute continuity I
• Spectral theory of extended Harper's model and a question by Erdős and Szekeres
• Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
• Singular continuous spectrum for singular potential
• Universal hierarchical structure of quasiperiodic eigenfunctions

Cited by in corpus (10)

• Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
• Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
• Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies
• Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum
• Almost Mathieu operators with completely resonant phases
• Discrete Bethe--Sommerfeld Conjecture for Triangular, Square, and Hexagonal Lattices
• Continuous quasiperiodic Schrödinger operators with Gordon type potentials
• Holder Continuity of Absolutely Continuous Spectral Measure for Multi-frequency Schrodinger Operators
• Spectral Dimension for $\beta$-almost periodic singular Jacobi operators and the extended Harper's model
• Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime