98-617 Dirk Buschmann, G\"unter Stolz

Two-Parameter Spectral Averaging and Localization for Non-Monotoneous Random Schr\"odinger Operators (70K, LaTeX) Sep 24, 98

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Abstract. We prove exponential localization at all energies for two types of one-dimensional random Schr\"odinger operators: the Poisson model and the random displacement model. As opposed to Anderson-type models, these operators are not monotoneous in the random parameters. Therefore the classical one-parameter version of spectral averaging, as used in localization proofs for Anderson models, breaks down. We use the new method of two-parameter spectral averaging and apply it to the Poisson as well as the displacement case. In addition, we apply results from inverse spectral theory, which show that two-parameter spectral averaging works for sufficiently many energies (all but a discrete set) to conclude localization at all energies.

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