Existence of the Density of States for Multi-Dimensional¶Continuum Schrödinger Operators with¶Gaussian Random Potentials

Abstract:

A Wegner estimate is proved for quantum systems in multi-dimensional Euclidean space which are characterized by one-particle Schrödinger operators with random potentials that admit a certain one-parameter decomposition. In particular, the Wegner estimate applies to systems with rather general Gaussian random potentials. As a consequence, these systems possess an absolutely continuous integrated density of states, whose derivative, the density of states, is locally bounded. An explicit upper bound is derived.