2017/06/30 by Adwait Gaikwad, Ritam Sinha
Mathematics · Physics and Astronomy · #Chaotic #Cold Atom Physics and Bose-Einstein Condensates #Eigenvalues and eigenvectors #Gaussian #Gaussian network model #Mathematics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Quantum mechanics #Quartic function #Random matrix #Statistical physics #Universality (dynamical systems) #hep-th
paper · pdf · doi:10.1103/physrevd.100.026017
published as Phys. Rev. D 100, 026017 (2019) · 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
arxiv created 2019/05/22 · openalex publication_date 2019/07/26 · arxiv updated 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider Random Matrix Theories with non-Gaussian potentials that have a rich phase structure in the large-N limit. We calculate the Spectral Form Factor (SFF) in such models and present them as interesting examples of dynamical models that display multicriticality at short timescales and universality at large timescales. The models with quartic and sextic potentials are explicitly worked out. The disconnected part of the Spectral Form Factor 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.