One plus two-body random matrix ensemble with spin: Analysis using spectral variances

For one plus two-body random matrix ensembles with spin, the chaos measure inverse participation ratio is calculated for 6, 7 and 8 fermion systems with good total spin S. Propagation equations for fixed-spin spectral variances explain the numerical results. Similarly, lower order correlations between spectra with different particle numbers and spins are analyzed using fixed-spin energy centroids and spectral variances. The correlations are found to be small for low-spin members.