Anderson Localization for Random Schrödinger Operators with Long Range Interactions
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- Kirsch, W., Stollmann, P. & Stolz, G. Commun. Math. Phys. (1998) 195: 495. doi:10.1007/s002200050399
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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 Vw(x) = Σqi(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 qi are supposed to be independent and identically distributed. We assume that their distribution has a bounded density of compact support.