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arXiv · 2608.11309

Spectrally local geometric response at the onset of many-body quantum chaos

George Mihailescu·Pablo M. Poggi
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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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George Mihailescu, Pablo M. Poggi. 2026-08-11. Spectrally local geometric response at the onset of many-body quantum chaos. https://arxiv.org/abs/2608.11309

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