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PreprintCC BY-NC-SA 4.0arXiv

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

  • Jan Fischer
  • David Hasler
  • Jannis Koberstein
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Abstract

We study a random Schrödinger 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.

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Cite

BibTeXRIS
BibTeX
@misc{fischer2026asymptotic,
  title = {{On asymptotic expansions of the density of states for Poisson distributed random Schrödinger operators}},
  author = {Jan Fischer and David Hasler and Jannis Koberstein},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11603},
  eprint = {2609.11603},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11603},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - On asymptotic expansions of the density of states for Poisson distributed random Schrödinger operators
AU  - Jan Fischer
AU  - David Hasler
AU  - Jannis Koberstein
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11603
UR  - https://arxiv.org/abs/2609.11603
AB  - We study a random Schrödinger 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.
ER  -