Spectral Form Factor in Non-Gaussian Random Matrix Theories
Abstract
We consider Random Matrix Theories with non-Gaussian potentials that have a rich phase structure in the large limit. We calculate the Spectral Form Factor (SFF) in such models and present them as interesting examples of dynamical models that display multi-criticality at short time-scales and universality at large time scales. The models with quartic and sextic potentials are explicitly worked out. The disconnected part of the Spectral Form Factor (SFF) shows a change in its decay behavior exactly at the critical points of each model. The dip-time of the SFF is estimated in each of these models. The late time behavior of all polynomial potential matrix models is shown to display a certain universality. This is related to the universality in the short distance correlations of the mean-level densities. We speculate on the implications of such universality for chaotic quantum systems including the SYK model.
Cite
@article{arxiv.1706.07439,
title = {Spectral Form Factor in Non-Gaussian Random Matrix Theories},
author = {Adwait Gaikwad and Ritam Sinha},
journal= {arXiv preprint arXiv:1706.07439},
year = {2019}
}
Comments
Introduction modified, section 2 moved to the Appendix, main text slightly modified, section on Paley-Wiener theorem omitted, new perspective on the results provided in sec V, typos corrected, footnotes added, references added, conclusion unchanged