Extended States for the Schrodinger Operator with Quasi-Periodic Potential in Dimension Two

Considers a Schrodinger operator $H=-Delta +V(vec x)$ in dimension two with a quasi-periodic potential $V(vec x)$. The authors prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties.