PreprintCC BY 4.0arXiv
Multifractal scaling of quantum eigenfunctions in the thermodynamic limit
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≥ 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.
Related
- Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps
- Scaling limit of the TASEP speed process
- Finite-volume and thermodynamic-limit lower bounds for the coherently driven Bose--Hubbard model via the Lieb--Yamazaki method
- Joint Scaling Limit of a Bipolar-Oriented Triangulation and Its Dual in the Peanosphere Sense
- The Thermodynamic Limit of Short-Range Spin Glasses with Periodic Boundary Conditions
BibTeX
@misc{keating2026multifractal,
title = {{Multifractal scaling of quantum eigenfunctions in the thermodynamic limit}},
author = {Jonathan P. Keating and Henrik Ueberschaer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08087},
eprint = {2611.08087},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08087},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multifractal scaling of quantum eigenfunctions in the thermodynamic limit
AU - Jonathan P. Keating
AU - Henrik Ueberschaer
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08087
UR - https://arxiv.org/abs/2611.08087
AB - 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≥ 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.
ER -