On asymptotic expansions of the density of states for Poisson distributed random Schrödinger operators

2022/08/02 by David Hasler, Hasler, David, Jannis Koberstein +1
Computer Science · Mathematics · Physics and Astronomy · #82B44 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2208.01578

openalex publication_date 2022/08/02 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

We study expectation values of matrix elements for boundary values of the resolvent as well as the density of states for a random Schrödinger 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.

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