The curious case of operators with spectral density increasing as $\Omega(E)\sim e^{\,\mathrm{Const.}\, E^2}$
General Relativity and Quantum Cosmology
2026-02-12 v1 Statistical Mechanics
Quantum Physics
Abstract
Motivated by a putative model of black holes as quantum objects we consider what types of operators would have a corresponding spectrum. We find that there are indeed such operators, but of a rather unusual types, and for which the wave functions are only barely localized. We point out a tension between such almost delocalized states and black holes as compact objects.
Cite
@article{arxiv.2504.06623,
title = {The curious case of operators with spectral density increasing as $\Omega(E)\sim e^{\,\mathrm{Const.}\, E^2}$},
author = {Erik Aurell and Satya N. Majumdar},
journal= {arXiv preprint arXiv:2504.06623},
year = {2026}
}
Comments
APS format, 5 pages, 50 references, no figures