97-72 Werner Kirsch, Peter Stollmann, G\"unter Stolz

Anderson Localization for Random Schr\"odinger Operators with Long Range Interactions (42K, LaTeX) Feb 12, 97

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Abstract. We prove pure point spectrum at all band edges for Schr\"odinger Operators with a periodic potential plus a random potential of the form $V_{\omega}(x) = \sum q_i(\omega) f(x-i)$ where $f$ is a long range interaction which decays at infinity like $|x|^{-m}$ for $m>3d$ respectively $m>2d$ depending on the regularity of $f$. We get power-decay for the eigenfunctions. The random variables $q_i$ are supposed to be independent and identically distributed. We suppose that their distribution has a bounded density of compact support.

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