Continuity properties of the integrated density of states on manifolds

Details Continuity properties of the integrated density of states on manifolds Continuity properties of the integrated density of states on manifolds

2007-05-08

arxiv.org/abs/0705.1079v1

Mathematics

Spectral Theory

35 pages, LaTeX 2e

Scientific paper

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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