Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)
Abstract
We introduce in this paper embedded Gaussian unitary ensemble of random matrices, for fermions in 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 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)- to EGUE(2)-SU(4) implying that symmetries may be responsible for chaos in finite interacting quantum systems.
Keywords
Cite
@article{arxiv.0904.0551,
title = {Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)},
author = {Manan Vyas and V. K. B. Kota},
journal= {arXiv preprint arXiv:0904.0551},
year = {2010}
}
Comments
11 pages, 2 figures, some formulas in Table 1 corrected, Table 1 changed to Table 1 and 2, Fig. 2 modified