 96648 Werner Kirsch, Peter Stollmann, G\"unter Stolz
 Localization for random perturbations of periodic Schr\"odinger operators
(96K, LaTeX)
Dec 6, 96

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Abstract. (This is a revised version of a preprint posted in 9/96.)
We prove localization for Andersontype random perturbations of
periodic Schr\"odinger operators on ${\bf R}^d$ near the band edges.
General, possibly unbounded, single site potentials of fixed sign and
compact support are allowed in the random perturbation. The proof is
based on the following methods:
(i) A study of the band shift of periodic Schr\"odinger operators
under linearly coupled periodic perturbations.
(ii) A proof of the Wegner estimate using properties of the
spatial distribution of eigenfunctions of finite box hamiltonians.
(iii) An improved multiscale method together with a result of de
Branges on the existence of limiting values for resolvents in the
upper half plane, allowing for rather weak disorder assumptions on the
random potential.
(iv) Results from the theory of generalized eigenfunctions and
spectral averaging.
The paper aims at high accessibility in providing details for all the
main steps in the proof.
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96648.tex