Random matrix ensemble with random two-body interactions in the presence of a mean field for spin-one boson systems.

For bosons carrying spin-one degree of freedom, we introduce an embedded Gaussian orthogonal ensemble of random matrices generated by random two-body interactions in the presence of a mean field that is spin (S) scalar [called BEGOE(1+2)-S1]. Embedding algebra for the ensemble, for m bosons in Ω number of single-particle levels (each triply degenerate), is U(3Ω)⊃G⊃G1⊗SO(3) with SO(3) generating the spin S. A method for constructing the ensemble for a given (Ω,m,S) has been developed. Numerical calculations show that (i) the form of the fixed-(m, S) density of states is close to a Gaussian; (ii) for a strong enough interaction, level fluctuations follow GOE; (iii) fluctuation in energy centroids is large; and (iv) spectral widths are nearly constant with respect to S for S<S(max)/2. Moreover, we identify two different pairing symmetry algebras in the space defined by BEGOE(1+2)-S1 and numerical results show that random interactions generate ground states with maximal value for the pair expectation value.