Embedded gaussian unitary ensembles: Results from wigner-racah algebra

Abstract

In this chapter, the GUE version of embedded ensembles (EGUE), both for fermion and boson systems, are considered and results from the Wigner-Racah algebra of the Lie algebras defining the embedding are presented. In particular, given is the general formulation for the lower order moments of the one- and two-point functions for the ensembles with U(Ω)⊠- SU(r) embedding and random two-body Hamiltonians with SU(r) symmetry. Results from this formulation are presented with examples for fermion systems with r=1, 2 and 4 and similarly, for boson systems with r=1, 2 and 3. In addition, results for the general spinless EGUE(k) and BEGUE(k) are also presented. © 2014 Springer International Publishing Switzerland.