Rigorous results on Schrödinger operators with certain Gaussian random potentials in multi-dimensional continuous space

Schrödinger operators with Gaussian random potentials in d-dimensional Euclidean space IR, d ≥ 1, find wide-spread applications in physics. They are used, for example, to model aspects of disordered electronic systems such as heavily doped and highly compensated semiconductors [BEE+, SE]. Over several decades theoretical physicists have developed a good insight into the spectral characteristics of these operators by combining intuitive ideas with approximation techniques and numerical studies. On the other hand there are still only few rigorous results available [K, CL, PF]. Our goal here is to present two new ones, which in the physics literature are often taken for granted. More precisely, for IR-homogeneous Gaussian random potentials with certain covariance functions we are able to prove (i) the existence of the density of states, that is, the absolute continuity of the integrated density of states and (ii) the almost-sure absence of the absolutely continuous spectrum at sufficiently low energies.