On asymptotic expansions of resolvents for Poisson distributed random Schrödinger operators

Abstract

We study expectation values of matrix elements of the resolvent for a random Schrödinger operator with potential distributed according to a Poisson process. Asymptotic expansions for these matrix elements of resolvents 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 finite as the spectral parameter approaches the spectrum of the free Laplacian.