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

Details The Density of States and the Spectral Shift Density of Random Schroedinger Operators The Density of States and the Spectral Shift Density of Random Schroedinger Operators

2000-11-18

arxiv.org/abs/math-ph/0011033v1

Reviews in Mathematical Physics 12 (2000) 807 - 847

Physics

Mathematical Physics

1 figure

Scientific paper

10.1142/S0129055X00000320

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.

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