aiqbench analysis
This research introduces the spectral density of geometric response as a novel metric for detecting early-stage transitions from integrability to chaos in many-body quantum systems. By demonstrating that eigenstate sensitivity accumulates locally before spreading, the study identifies universal features absent in standard Gaussian random-matrix models while highlighting the necessity of physically motivated ensembles. These findings advance fundamental understanding of spectral statistics and dynamical complexity within isolated quantum systems.
Spectrally local geometric response at the onset of many-body quantum chaos
arXiv:2608.11309v2 Announce Type: replace 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.
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.
5 pages, 4 figures. Includes Supplementary Material (6 pages + 3 figures). We kindly welcome comments and suggestions
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2608.11309 [quant-ph]
(or arXiv:2608.11309v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.11309 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 183 words
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