Smooth spectral statistics of random perturbations of Schrödinger operators near Anosov energy levels
Year: 2026
Type: preprint
Abstract: We investigate the spectral statistics of random perturbations of semiclassical Schrödinger operators on compact manifolds, near energy levels corresponding to chaotic classical dynamics. The prototypical example is that of an operator $h^2Δ+V(x)$ that is perturbed by a smooth potential $h^αV_ω$ with $α\in (0,1)$, and $V_ω$ is a random potential that decorrelates on distances $h^β$, with $0<β<2α$. We show that for a generic perturbation, the spectral fluctuations of the smoothed counting function of eigenvalues obey a universal behavior at a certain mesoscopic scale, which is coherent with the predictions of random matrix theory.
Source: arXiv (Cornell University)
Author: Moy, Julien
Institutions: Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221056639