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Quantum Foundations

Crystalline Spectral Form Factors

arXiv
Authors: Dmitrii A. Trunin, David A. Huse

Year

2025

Paper ID

36673

Status

Preprint

Abstract Read

~2 min

Abstract Words

96

Citations

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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  • We investigate crystalline-like behavior of the spectral form factor (SFF) in unitary quantum systems with extremely strong eigenvalue repulsion.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.11054 [2] arXiv https://arxiv.org/abs/2512.11054 [3] Publisher https://arxiv.org/abs/2512.11054

Local Citation Graph (Related-Paper Links)

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External citation index: OpenAlex citation signal • updated 2026-11-06 01:00:17

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