Continuity of the Lyapunov Exponent for analytic quasi-perodic cocycles with singularities

TL;DR

This paper proves the continuity of the Lyapunov exponent for analytic quasi-periodic cocycles with singularities, extending previous results and applying to models like the extended Harper's model in physics.

Contribution

It generalizes earlier continuity results by allowing singularities in quasi-periodic cocycles, broadening the scope of applicable models.

Findings

Lyapunov exponent is continuous over the analytic category with singularities

Extends previous results excluding or constraining singularities

Applicable to models like extended Harper's model in physics

Abstract

We prove that the Lyapunov exponent of quasi-periodic cocyles with singularities behaves continuously over the analytic category. We thereby generalize earlier results, where singularities were either excluded completely or constrained by additional hypotheses. Applications are one-parameter families of analytic Jacobi operators, such as extended Harper's model describing crystals subject to external magnetic fields.