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

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.

arXiv comment4 pages

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• Eigenfunction statistics of Laguerre Brownian ensemble
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• Random matrix ensembles: Wang-Landau algorithm for spectral densities
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• Spectral and Strength Statistics of Chiral Brownian Ensemble
• Many body density of states in the edge of the spectrum: non-interacting limit