Georgia Institute of Technology College of Sciences

We present joint work with Artur Avila on delocalizing Schr\"odinger operators in arbitrary dimensions via arbitrarily small perturbations of the potential. As a consequence we obtain an analog of Simon's Wonderland Theorem for the case of dynamically defined potentials. We will discuss a mechanism based on the Feynman-Hellmann Theorem, whose infinite volume limit is instrumental in establishing delocalization in infinite volume. Furstenberg's correspondence principle then yields the desired delocalization statement in finite volume.