Wegner Estimate for Indefinite Anderson Potentials: Some Recent Results and Applications

Details Wegner Estimate for Indefinite Anderson Potentials: Some Recent Results and Applications Wegner Estimate for Indefinite Anderson Potentials: Some Recent Results and Applications

2005-10-17

arxiv.org/abs/math-ph/0510061v1

Lecture Notes of Research Institute for Mathematical Sciences, Kyoto University, volume 1275, (2002), 65--84

Physics

Mathematical Physics

20 pages, Proceedings of Conference ``Renormalization Group Methods in Mathematical Sciences'' RIMS, Kyoto, July 2001

Scientific paper

We review recent and give some new results on the spectral properties of Schroedinger operators with a random potential of alloy type. Our point of interest is the so called Wegner estimate in the case where the single site potentials change sign. The indefinitness of the single site potential poses certain difficulties for the proof of the Wegner estimate which are still not fully understood. The Wegner estimate is a key ingredient in an existence proof of pure point spectrum of the considered random Schroedinger operators. Under certain assumptions on the considered models additionally the existence of the density of states can be proven.

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