Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications. (1st December 2022) - Li, Xianzhe
Abstract: We establish a quantitative version of strong almost reducibility result for S L ( 2, R ) quasi-periodic cocycle close to a constant in the Gevrey class. We prove that, if the frequency is Diophantine, the long range operator has pure point spectrum with sub-exponentially decaying eigenfunctions for almost all phases; for the one dimensional quasi-periodic Schrödinger operators with small Gevrey potentials, the length of spectral gaps decays sub-exponentially with respect to its labelling; and the spectrum is an interval for discrete Schrödinger operators acting on Z d with small separable potentials.