Abstract
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.
Funder
Nankai Zhide Foundation
National Key R&D Program of China
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Reference62 articles.
1. Hölder continuity of the rotation number for quasi-periodic co-cycles in SL(2,R);Amor;Commun. Math. Phys.,2009
2. Cantor sets and numbers with restricted partial quotients;Astels;Trans. Am. Math. Soc.,2000
3. Analyticity breaking and Anderson localization in incommensurate lattices;Aubry;Ann. Isr. Phys. Soc.,1980
4. The absolutely continuous spectrum of the almost Mathieu operator;Avila,2008
5. A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies;Avila;Geom. Funct. Anal.,2011