Universal Spectral Correlations in Orthogonal-Unitary and Symplectic-Unitary Crossover Ensembles of Random Matrices

TL;DR

This paper demonstrates that universal spectral correlation functions in orthogonal-unitary and symplectic-unitary crossover ensembles of random matrices are consistent across different matrix families and exhibit universality in large matrix limits.

Contribution

It extends the universality of spectral correlations to the Jacobi family of crossover ensembles using skew-orthogonal polynomials.

Findings

Universal n-level correlation functions for Jacobi crossover ensembles.

Formulas applicable to Laguerre and Gaussian cases.

Universal large-matrix correlation functions in terms of a rescaled transition parameter.

Abstract

Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we show that the same generic form of n-level correlation functions are obtained for the Jacobi family of crossover ensembles, including the Laguerre and Gaussian cases. For large matrices we find universal forms of unfolded correlation functions when expressed in terms of a rescaled transition parameter with arbitrary initial level density.