Random matrix theory signatures in free field theory

Dmitry S. Ageev; Vasilii V. Pushkarev

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arXiv · 2507.18746

Random matrix theory signatures in free field theory

Dmitry S. Ageev·Vasilii V. Pushkarev

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Abstract

We show that, within a finite window of parameter space, random matrix theory (RMT) statistics emerge in observables of a finite-volume massive free scalar field theory after a local operator quench. The spacing-ratio distribution of two-point-function extremum locations is close to the Gaussian orthogonal ensemble statistics. An extrema-based form factor exhibits a dip--ramp--plateau structure characteristic of RMT. By contrast, the standard spectral form factor shows no ramp, consistent with the underlying free spectrum, while a global quench yields qualitatively different statistics.

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Dmitry S. Ageev, Vasilii V. Pushkarev. 2025-07-24. Random matrix theory signatures in free field theory. https://arxiv.org/abs/2507.18746

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