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arXiv · 2611.08087

Multifractal scaling of quantum eigenfunctions in the thermodynamic limit

Jonathan P. Keating·Henrik Ueberschaer
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Abstract

We prove multifractal scaling of measures related to the eigenfunctions of Schrödinger operators with point-like bump potentials, in the thermodynamic limit, in dimension $d\geq 5$. This is consistent with a longstanding expectation in the physics literature in these dimensions. The fractal exponents are computed explicitly as a function of the parameter defining the moments. Our result requires a weak disorder condition on the location of the scatterers and a strong coupling condition on the sequence of eigenvalues.

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Jonathan P. Keating, Henrik Ueberschaer. 2026-11-05. Multifractal scaling of quantum eigenfunctions in the thermodynamic limit. https://arxiv.org/abs/2611.08087

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