Anderson Localization for Random Schrödinger Operators with Long Range Interactions

Abstract:

We prove pure point spectrum with exponentially decaying eigenfunctions at all band edges for Schrödinger Operators with a periodic potential plus a random potential of the form V _w (x) = Σq _i (w)f(x - i), where $f$ decays at infinity like |x|^−m for m>4d resp. $m>3d depending on the regularity of f. The random variables q _i are supposed to be independent and identically distributed. We assume that their distribution has a bounded density of compact support.