Density of states for the Anderson model on nested fractals

Hubert Balsam; Kamil Kaleta; Mariusz Olszewski; Katarzyna Pietruska-Pałuba

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arXiv · 2303.05980

Density of states for the Anderson model on nested fractals

Hubert Balsam·Kamil Kaleta·Mariusz Olszewski·Katarzyna Pietruska-Pałuba

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Abstract

We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians $H^\omega=H_0+V^\omega$ on fractal spaces of infinite diameter. The kinetic term $H_0$ is given by $\phi(-\mathcal L),$ where $\mathcal L$ is the Laplacian on the fractal and $\phi$ is a completely monotone function satisfying some mild regularity conditions. The random potential $V^\omega$ is of alloy-type.

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BibTeX RIS

Hubert Balsam, Kamil Kaleta, Mariusz Olszewski, Katarzyna Pietruska-Pałuba. 2023-03-10. Density of states for the Anderson model on nested fractals. https://arxiv.org/abs/2303.05980

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