标题： 态密度和随机薛定谔算子的谱移密度 显示英文标题

标题： The Density of States and the Spectral Shift Density of Random Schroedinger Operators

摘要： 在本文中，我们继续使用散射理论对具有随机势的薛定谔算子进行分析。 特别是克雷因的谱位移函数理论导致了任意维数下状态密度的另一种构造方法。 对于任意维数，我们证明了谱位移密度的存在性，该密度定义为单位相互作用体积的谱位移函数的体极限。 该密度等于自由理论和相互作用理论的状态密度之差。 这扩展了作者之前在一维情况下获得的结果。 此外，我们还考虑了相互作用集中在超平面附近的特殊情况。 显示英文摘要

摘要： In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.