Upper bounds on eigenvalue spacing for decaying potentials
Spectral Theory
2026-01-30 v1 Classical Analysis and ODEs
Abstract
We study decaying half-line Schr\"odinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with bulk universality and clock behavior, singular spectral measures can correspond to varied local behaviors. In this work, the rate of decay of the potential is shown to give upper bounds for the spacing of Dirichlet eigenvalues on finite intervals.
Cite
@article{arxiv.2601.21108,
title = {Upper bounds on eigenvalue spacing for decaying potentials},
author = {Milivoje Lukic and Brian Simanek},
journal= {arXiv preprint arXiv:2601.21108},
year = {2026}
}
Comments
Dedicated to Barry Simon on the occasion of his 80th birthday