Approximating the density of states for Poisson distributed random Schroedinger operators

2023/02/10 by David Hasler, Hasler, David, Jannis Koberstein +1
Computer Science · Mathematics · Physics and Astronomy · #46 #47 #81 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2302.05234

openalex publication_date 2023/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a Schroedinger operator with random potential distributed according to a Poisson process. We show that expectations of matrix elements of the resolvent as well as the density of states can be approximated to arbitrary precision in powers of the coupling constant. The expansion coefficients are given in terms of expectations obtained by Neumann expanding the potential around the free Laplacian. One can control these expansion coefficients in the infinite volume limit. We show that for this limit the boundary value as the spectral parameter approaches the real axis exists as well. Our results are valid for arbitrary strength of the disorder parameter, including the small disorder regime.

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