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Continuity properties of the integrated density of states on manifolds |
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| Authors: | Daniel Lenz Norbert Peyerimhoff Olaf Post Ivan Veselić |
| Affiliation: | 1. Fakult?t für Mathematik, TU Chemnitz, D-09107, Chemnitz, Germany 2. Department of Mathematical Sciences, Durham University, Science Laboratories South Road, Durham, DH1 3LE, Great Britain 3. Institut für Mathematik, Humboldt-Universit?t zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany 4. Emmy-Noether Programme of the DFG, Fakult?t für Mathematik, TU Chemnitz, D-09107, Chemnitz, Germany |
| Abstract: | We first analyze the integrated density of states (IDS) of periodic Schrödinger 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. |
| Keywords: | integrated density of states periodic and random operators Schr?dinger operators on manifolds continuity properties |
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