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Smooth spectral statistics of random perturbations of Schrödinger operators near Anosov energy levels
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 h2Δ+V(x) that is perturbed by a smooth potential hαVω with α∈ (0,1), and Vω is a random potential that decorrelates on distances hβ, 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.
Related
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BibTeX
@misc{moy2026smooth,
title = {{Smooth spectral statistics of random perturbations of Schrödinger operators near Anosov energy levels}},
author = {Julien Moy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09869},
eprint = {2610.09869},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09869},
}
RIS
TY - UNPB
TI - Smooth spectral statistics of random perturbations of Schrödinger operators near Anosov energy levels
AU - Julien Moy
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09869
UR - https://arxiv.org/abs/2610.09869
AB - 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∈ (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.
ER -