Two-body ensembles with group symmetries for chaos and regular structures

摘要

The simplest of the two-body random matrix ensembles (TBRE) is the embedded Gaussian orthogonal ensemble of two-body interactions [EGOE(2)] for spinless fermion systems. With m fermions in N single particle states, EGOE(2) and similarly EGUE(2) [the embedded Gaussian unitary ensemble] are generated by the SU(N) algebra. For these ensembles results, obtained using SU(N) Wigner-Racah algebra, for lower order cross correlations between spectra with different particle numbers are given. For fermions with spin degree of freedom one has EGOE(2)-s and similarly EGUE(2)-s, both generated by U(20) D U(Q) 0 SU(2) algebra with SU(2) generating m particle spins S and 2 Omega = N. For these ensembles numerical and first analytical results for cross correlations between spectra with different particle numbers and spins are given. As further extensions, it is possible to construct EGOE(2)-(s,p) generated by U(2 Omega) D [U(Omega) superset of SO(Omega)] circle times SU(2) where SO(Omega) corresponds to pairing, for nuclear shell model the EGOE(2)-JT generated by U(N) superset of SOJ(3) circle times SUT(2) algebra etc. On the other hand EGOE's with extended group symmetries of the shell model and the interacting boson models of nuclei, in particular via trace propagation for energy centroids give new insights into regular structures seen in the ground state region of nuclei. Several new examples for energy centroids generated by random 2 and 3-body interactions are given.