Searcharxiv⌕ Search

arXiv subjects

Jannis Koberstein

Publications and source records attributed to Jannis Koberstein.

5 recordsLinked to original sources
arXiv2026

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

We study a random Schr\"odinger operator with a potential distributed according to a Poisson process. Asymptotic expansions for traces 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. As an application we derive bounds on the integrated density of states.

math-ph↗
arXiv2023

Approximating the density of states for Poisson distributed random Schroedinger operators

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.

math-ph↗
arXiv2022

On asymptotic expansions of resolvents for Poisson distributed random Schr\"odinger operators

We study expectation values of matrix elements of the resolvent for a random Schr\"odinger 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.

math-ph↗