Continuity properties of the integrated density of states on manifolds
D. LenzCN. PeyerimhoffCO. PostCI. Veselić
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.