SU(N) Wigner-Racah algebra for the matrix of second moments of embedded Gaussian unitary ensemble of random matrices

Abstract

Recently Pluhar and Weidenmueller [Ann. Phys. (N.Y.) Vol 297, 344 (2002)] showed that the eigenvectors of the matrix of second moments of embedded Gaussian unitary ensemble of random matrices generated by k-body interactions (EGUE(k)) for m fermions in N single particle states are SU(N) Wigner coefficients and derived also an expression for the eigenvalues. Going beyond this work, we will show that the eigenvalues of this matrix are square of a SU(N) Racah coefficient and thus the matrix of second moments of EGUE(k) is solved completely by SU(N) Wigner-Racah algebra.

16 pages

References in corpus (3)

• Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
• Distribution of spectral widths and preponderance of spin-0 ground states in nuclei
• Odd-even binding effect from random two-body interactions

Cited by in corpus (7)

• The Two-Body Random Ensemble in Nuclei
• Quenched many-body quantum dynamics with $k$-body interactions using $q$-Hermite polynomials
• Embedded Gaussian Unitary Ensembles with $U(\Omega )\otimes SU(r)$ Embedding generated by Random Two-body Interactions with $SU(r)$ Symmetry
• Two species $k$-body embedded Gaussian unitary ensembles: $q$-normal form of the eigenvalue density
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions
• Group Theory for Embedded Random Matrix Ensembles
• Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)