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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21386 |
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| _version_ | 1866915708250619904 |
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| author | Altland, Alex Divi, Francisco Micklitz, Tobias Pappalardi, Silvia Rezaei, Maedeh |
| author_facet | Altland, Alex Divi, Francisco Micklitz, Tobias Pappalardi, Silvia Rezaei, Maedeh |
| contents | The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$, have recently come to attention, with conflicting results in the literature. In this work, we investigate these departures from Gaussianity for both circular and Gaussian ensembles. Using two independent approaches -- sine-kernel techniques and supersymmetric field theory -- we identify the form factor statistics to next leading order in a $D^{-1}$ expansion. Our sine-kernel analysis highlights inconsistencies with previous studies, while the supersymmetric approach backs these findings and suggests an understanding of the statistics from a complementary perspective. Our findings fully agree with numerics. They are presented in a pedagogical way, highlighting new pathways (and pitfalls) in the study of statistical signatures at next leading order, which are increasingly becoming important in applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21386 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistics of the Random Matrix Spectral Form Factor Altland, Alex Divi, Francisco Micklitz, Tobias Pappalardi, Silvia Rezaei, Maedeh Quantum Physics Disordered Systems and Neural Networks High Energy Physics - Theory The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$, have recently come to attention, with conflicting results in the literature. In this work, we investigate these departures from Gaussianity for both circular and Gaussian ensembles. Using two independent approaches -- sine-kernel techniques and supersymmetric field theory -- we identify the form factor statistics to next leading order in a $D^{-1}$ expansion. Our sine-kernel analysis highlights inconsistencies with previous studies, while the supersymmetric approach backs these findings and suggests an understanding of the statistics from a complementary perspective. Our findings fully agree with numerics. They are presented in a pedagogical way, highlighting new pathways (and pitfalls) in the study of statistical signatures at next leading order, which are increasingly becoming important in applications. |
| title | Statistics of the Random Matrix Spectral Form Factor |
| topic | Quantum Physics Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.21386 |