Crystalline Spectral Form Factors
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908739804594176 |
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| author | Trunin, Dmitrii A. Huse, David A. |
| author_facet | Trunin, Dmitrii A. Huse, David A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crystalline Spectral Form Factors Trunin, Dmitrii A. Huse, David A. Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Chaotic Dynamics Cellular Automata and Lattice Gases 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. |
| title | Crystalline Spectral Form Factors |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Chaotic Dynamics Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2512.11054 |