Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
The spectral-averaging technique is used to prove the absolute continuity of the integrated density of states for a Schrödinger operator with a rather general Gaussian random potential in multidimensional Euclidean space. As a consequence, an explicit upper bound for the density of states is derived. The result is based on the Wegner estimate [\textit{F. Wegner}, Z. Phys. B 44, 9-15 (1981)] which is proved to hold for all continuum Schrödinger operators whose random potential admits a certain one-parameter decomposition. The present paper accomplishes partly the localization proofs announced by the authors in \textit{W. Fischer}, \textit{H. Leschke} and \textit{P. Müller} [Lett. Math. Phys. 38, No. 4, 343-348 (1996; Zbl 0862.60047)]. The authors remark their results can be extended to random Schrödinger operators with rather general magnetic fields.
scientific article; zbMATH DE number 1121344