Abstract
We consider Schrödinger operators $H=-\Delta+V(\mathbf{x)}$ in $\mathbb{R}^d$, $d\ge 2$, with quasi periodic potentials $V(\mathbf{x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis $[\lambda_*,+\infty)$. We also construct a family of eigenfunctions of the absolutely continuous spectrum; these eigenfunctions are small perturbations of the exponentials. The proof is based on a version of the multi-scale analysis in the momentum space with several new ideas introduced along the way.
