2000/06/01 by Vadim Kostrykin, VADIM KOSTRYKIN, Robert Schrader +1 · 2 citations
Mathematics · Physics and Astronomy · #Holomorphic and Operator Theory #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35J10 #msc:35Q40 #msc:47B80
paper · pdf · doi:10.1142/s0129055x00000320
published as Reviews in Mathematical Physics 12 (2000) 807 - 847 · 1 figure
openalex publication_date 2000/06/01 · arxiv created 2000/11/18 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this article we continue our analysis of Schrödinger 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.