Upper bounds on eigenvalue spacing for decaying potentials
Abstract
We study decaying half-line Schrödinger 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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Random Matrices and Applications
Quantum chaos and dynamical systems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 January 2026
- Document type
- Preprint