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

• URL: http://arxiv.org/abs/2608.11309v2
• Date: Sun, 16 Aug 2026 22:33:19 GMT
• Title: Spectrally local geometric response at the onset of many-body quantum chaos
• Abstract summary: We introduce the spectral density of geometric response, a measure of eigenstate sensitivity across an energy spectrum.<n>It reveals an exponentially sensitive integrability-to-chaos crossover, where eigenbasis deformations first accumulate in localized spectral regions before spreading throughout the spectrum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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