$L^2$reducibility and localization for quasiperiodic operators
Abstract
We give a simple argument that if a quasiperiodic multifrequency Schrödinger cocycle is reducible to a constant rotation for almost all energies with respect to the density of states measure, then the spectrum of the dual operator is purely point for Lebesgue almost all values of the ergodic parameter $\theta$. The result holds in the $L^2$ setting provided, in addition, that the conjugation preserves the fibered rotation number. Corollaries include localization for (longrange) 1D analytic potentials with dual ac spectrum and Diophantine frequency as well as a new result on multidimensional localization.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.07149
 Bibcode:
 2015arXiv150507149J
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Dynamical Systems
 EPrint:
 9 pages