Crystalline Spectral Form Factors

• URL: http://arxiv.org/abs/2512.11054v1
• Date: Thu, 11 Dec 2025 19:11:26 GMT
• Title: Crystalline Spectral Form Factors
• Authors: Dmitrii A. Trunin, David A. Huse,
• Abstract summary: We investigate crystalline-like behavior of the spectral form factor (SFF) in unitary quantum systems with strong eigenvalue repulsion.<n>We derive the Debye-Waller factor suppressing periodic oscillations of the SFF and estimate the order of its singularities at multiples of the Heisenberg time.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate crystalline-like behavior of the spectral form factor (SFF) 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 SFF 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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