The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances

Abstract

We prove that for any given frequency resonance exponent and phase resonance exponent, there exist a frequency and a phase exactly realizing these values such that the Almost Mathieu operator exhibits Anderson localization for $\ln|λ|>\max\{β(α),δ(α,θ)\}$. This resolves the conjecture in \cite{MR4686650}.