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.
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Received: 9 April 1997 / Accepted: 5 December 1997
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Kirsch, W., Stollmann, P. & Stolz, G. Anderson Localization for Random Schrödinger Operators with Long Range Interactions . Commun. Math. Phys. 195, 495–507 (1998). https://doi.org/10.1007/s002200050399
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DOI: https://doi.org/10.1007/s002200050399