Statistics of the Random Matrix Spectral Form Factor

• URL: http://arxiv.org/abs/2503.21386v1
• Date: Thu, 27 Mar 2025 11:34:12 GMT
• Title: Statistics of the Random Matrix Spectral Form Factor
• Authors: Alex Altland, Francisco Divi, Tobias Micklitz, Silvia Pappalardi, Maedeh Rezaei,
• Abstract summary: We identify the form factor statistics to next leading order in a $D-1$ expansion.<n>Our findings fully agree with numerics.<n>They are presented in a pedagogical way, highlighting new pathways in the study of statistical signatures at next leading order.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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