PreprintCC BY 4.0arXiv
Spectrally local geometric response at the onset of many-body quantum chaos
Abstract
We introduce the spectral density of geometric response, a measure of eigenstate sensitivity across an energy spectrum. Applied to many-body quantum systems, it reveals an exponentially sensitive integrability-to-chaos crossover, where eigenbasis deformations first accumulate in localized spectral regions before spreading throughout the spectrum. Physically motivated random-matrix ensembles reproduce this behaviour, whereas Gaussian ensembles do not, indicating universal features of the route to chaos that are absent from featureless random-matrix models.
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BibTeX
@misc{mihailescu2026spectrally,
title = {{Spectrally local geometric response at the onset of many-body quantum chaos}},
author = {George Mihailescu and Pablo M. Poggi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.11309},
eprint = {2608.11309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11309},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectrally local geometric response at the onset of many-body quantum chaos
AU - George Mihailescu
AU - Pablo M. Poggi
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.11309
UR - https://arxiv.org/abs/2608.11309
AB - We introduce the spectral density of geometric response, a measure of eigenstate sensitivity across an energy spectrum. Applied to many-body quantum systems, it reveals an exponentially sensitive integrability-to-chaos crossover, where eigenbasis deformations first accumulate in localized spectral regions before spreading throughout the spectrum. Physically motivated random-matrix ensembles reproduce this behaviour, whereas Gaussian ensembles do not, indicating universal features of the route to chaos that are absent from featureless random-matrix models.
ER -