Large coupling asymptotics for the Lyapunov exponent of quasi-periodic Schr\"odinger operators with analytic potentials

TL;DR

This paper refines the understanding of how the Lyapunov exponent behaves in the large coupling limit for a class of quasi-periodic Schrödinger operators with analytic potentials, providing more precise asymptotic estimates.

Contribution

It improves the known lower bounds on the Lyapunov exponent's asymptotics for these operators, offering a more detailed quantification of coupling effects.

Findings

Refined asymptotic estimates for the Lyapunov exponent at large coupling

Improved lower bounds compared to previous results by Sorets and Spencer

Enhanced understanding of spectral properties of quasi-periodic Schrödinger operators

Abstract

We quantify the coupling asymptotics for the Lyapunov-exponent of a one-frequency quasi-periodic Schr\"odinger operator with analytic potential sampling function. The result refines the well-known lower bound of the Lyapunov-exponent by Sorets and Spencer.