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arXiv · 0705.1079

Continuity properties of the integrated density of states on manifolds

Daniel Lenz·Norbert Peyerimhoff·Olaf Post·Ivan Veselic'
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Abstract

We first analyze the integrated density of states (IDS) of periodic Schr\"odinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous "periodic" IDS which is regularized by a random perturbation.

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BibTeXRIS

Daniel Lenz, Norbert Peyerimhoff, Olaf Post, Ivan Veselic'. 2007-05-08. Continuity properties of the integrated density of states on manifolds. https://doi.org/10.1007/s11537-008-0729-4

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