Density of states for the Anderson model on nested fractals

We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians H ω = H 0 + V ω on fractal spaces of infinite diameter. The kinetic term H 0 is given by ϕ ( - L ) , where L is the Laplacian on the fractal and ϕ is a completely monoto...

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Bibliographic Details
Published in:Analysis and mathematical physics 2024-04, Vol.14 (2), Article 23
Main Authors: Balsam, Hubert, Kaleta, Kamil, Olszewski, Mariusz, Pietruska-Pałuba, Katarzyna
Format: Article
Language:English
Subjects:
Analysis
Density of states
Fractal models
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary:We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians H ω = H 0 + V ω on fractal spaces of infinite diameter. The kinetic term H 0 is given by ϕ ( - L ) , where L is the Laplacian on the fractal and ϕ is a completely monotone function satisfying some mild regularity conditions. The random potential V ω is of alloy-type.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-024-00880-8