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arXiv · 2609.17075

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. Isotropic$α$-stable Lévy processes are self-similar but not continuous. Thus self-similarity is a fundamental concept for these quantum operators.

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Peter Kern, Leonard Pleschberger. 2026-09-15. On the Integrated Density of States of Fractional Random Schrödinger Operators. https://arxiv.org/abs/2609.17075

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