Spectral form factors and late time quantum chaos
Junyu Liu
TL;DR
This paper reviews spectral form factors of various random matrix ensembles and discusses their relevance to late time quantum chaos, providing practical insights for current research.
Contribution
It offers a comprehensive collection of spectral form factor results for multiple ensembles, aiding the study of late time quantum chaos.
Findings
Spectral form factors characterized for GUE, GOE, GSE, LUE, LOE, and LSE.
Classification of late time quantum chaos based on spectral form factors.
Practical applications in quantum chaos research.
Abstract
This is a collection of notes that are about spectral form factors of standard ensembles in the random matrix theory, written for the practical usage of current study of late time quantum chaos. More precisely, we consider Gaussian Unitary Ensemble (GUE), Gaussian Orthogonal Ensemble (GOE), Gaussian Symplectic Ensemble (GSE), Wishart-Laguerre Unitary Ensemble (LUE), Wishart-Laguerre Orthogonal Ensemble (LOE), and Wishart-Laguerre Symplectic Ensemble (LSE). These results and their physics applications cover a three-fold classification of late time quantum chaos in terms of spectral form factors.
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