Statistics

Laguerre polynomials

Circular ensemble

Physics

Statistical physics

Quantum chaos

Quantum dynamics

Eigenvalues and eigenvectors

Multivariate statistics

Gaussian

Symplectic geometry

Political science

Monte Carlo method

Pure mathematics

Canonical ensemble

Mathematics

Wishart distribution

Statistical ensemble

Quantum mechanics

Random matrix

Unitary state

Quantum

Physical review. D/Physical review. D.

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.

Spectral form factors and late time quantum chaos