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PreprintCC BY 4.0arXiv

On the Integrated Density of States of Fractional Random Schrödinger Operators

  • Peter Kern
  • Leonard Pleschberger
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Abstract

We proof the existence of the Integrated Density of States (IDS) for fractional random Schrödinger operators with Gaussian potential based on the theory of isotropic α-stable Lévy processes. Further we show that the IDS exhibits Lifshitz tails and determine its asymptotics at the right end of the spectrum. Isotropicα-stable Lévy processes are self-similar but not continuous. Thus self-similarity is a fundamental concept for these quantum operators.

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Cite

BibTeXRIS
BibTeX
@misc{kern2026integrated,
  title = {{On the Integrated Density of States of Fractional Random Schrödinger Operators}},
  author = {Peter Kern and Leonard Pleschberger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17075},
  eprint = {2609.17075},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17075},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Integrated Density of States of Fractional Random Schrödinger Operators
AU  - Peter Kern
AU  - Leonard Pleschberger
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.17075
UR  - https://arxiv.org/abs/2609.17075
AB  - We proof the existence of the Integrated Density of States (IDS) for fractional random Schrödinger operators with Gaussian potential based on the theory of isotropic α-stable Lévy processes. Further we show that the IDS exhibits Lifshitz tails and determine its asymptotics at the right end of the spectrum. Isotropicα-stable Lévy processes are self-similar but not continuous. Thus self-similarity is a fundamental concept for these quantum operators.
ER  -