On asymptotic expansions of the density of states for Poisson distributed random Schr\"odinger operators

Abstract

We study expectation values of matrix elements for boundary values of the resolvent as well as the density of states for a random Schr\"odinger operator with potential distributed according to a Poisson process. Asymptotic expansions for these quantities in the limit of small disorder are derived. Explicit estimates for the expansion coefficients are given and we show that their infinite volume limits are in fact finite as the spectral parameter approaches the spectrum of the free Laplacian.