Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495919 | Journal of Functional Analysis | 2005 | 38 Pages |
Abstract
In this paper we consider the discrete one-dimensional Schrödinger operator with quasi-periodic potential vn=λv(x+nÏ). We assume that the frequency Ï satisfies a strong Diophantine condition and that the function v belongs to a Gevrey class, and it satisfies a transversality condition. Under these assumptions we prove-in the perturbative regime-that for large disorder λ and for most frequencies Ï the operator satisfies Anderson localization. Moreover, we show that the associated Lyapunov exponent is positive for all energies, and that the Lyapunov exponent and the integrated density of states are continuous functions with a certain modulus of continuity. We also prove a partial nonperturbative result assuming that the function v belongs to some particular Gevrey classes.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Silvius Klein,