Random matrix ensembles with random interactions:

Results for EGUE(2)-SU(4)

MANAN VYAS¹ and V K B KOTA^1,2,*

¹Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India

²Department of Physics, Laurentian University, Sudbury, ON P3E 2C6, Canada

^*Corresponding author. E-mail: vkbkota@prl.res.in

Abstract. We introduce in this paper embedded Gaussian unitary

ensemble of random matrices, for $m$ fermions in $\Omega$ number of

single particle orbits, generated by random two-body interactions

that are $SU(4)$ scalar, called EGUE(2)-$SU(4)$. Here the $SU(4)$

algebra corresponds to Wigner's supermultiplet $SU(4)$ symmetry in

nuclei. Formulation based on Wigner--Racah algebra of the embedding

algebra $U(4\Omega) \supset U(\Omega) \otimes SU(4)$ allows for

analytical treatment of this ensemble and using this analytical

formulas are derived for the covariances in energy centroids and

spectral variances. It is found that these covariances increase in

magnitude as we go from EGUE(2) to EGUE(2)-$\cs$ to EGUE(2)-$SU(4)$

implying that symmetries may be responsible for chaos in finite

interacting quantum systems.

Keywords. Embedded ensembles; random interactions; EGUE(2);

EGUE(2)-$\cs$; EGUE(2)-$SU(4)$; Wigner--Racah algebra; covariances;

chaos.

PACS Nos 05.30.-d; 05.30.Fk; 21.60.Fw; 24.60.Lz