Existence of the density of states for some alloy type models with single site potentials of changing sign

Details Existence of the density of states for some alloy type models with single site potentials of changing sign Existence of the density of states for some alloy type models with single site potentials of changing sign

2002-04-15

arxiv.org/abs/math-ph/0204031v1

Physics

Mathematical Physics

9 pages, a different version to appear in proceedings of the Conference on Applied Mathematics and Scientific Computing, Dubro

Scientific paper

We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate we prove implies Anderson localization under certain additional assumptions. For some examples we discuss briefly some properties of the common and conditional densities of the random coupling constants used in the proof of the Wegner estimate.

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