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arXiv · 2512.11054

Crystalline Spectral Form Factors

Dmitrii A. Trunin·David A. Huse
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Abstract

We investigate crystalline-like behavior of the spectral form factor in unitary quantum systems with extremely strong eigenvalue repulsion. Using a low-temperature Coulomb gas as a model of repulsive eigenvalues, we derive the Debye-Waller factor suppressing periodic oscillations of the spectral form factor and estimate the order of its singularities at multiples of the Heisenberg time. We also reproduce this crystalline-like behavior using perturbed permutation circuits and random matrix ensembles associated with Lax matrices. Our results lay a foundation for future studies of quantum systems that exhibit intermediate level statistics between standard random matrix ensembles and permutation circuits.

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Dmitrii A. Trunin, David A. Huse. 2025-12-11. Crystalline Spectral Form Factors. https://doi.org/10.1103/94cc-zdbl

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