Onset of chaos in finite interacting Boson systems with F-spin

For m bosons, carrying spin (f = 1 2) degree of freedom, in Ω single particle levels which are doubly degenerate, one-plus two-body Embedded Gaussian Orthogonal random matrix Ensemble which conserves spin (F) [BEGOE(1 + 2)-F] is defined and spectral properties are examined. Using mean field defined by random single particle energies, for fixed-(m,F) BEGOE(1 + 2)-F, density of states being close to Gaussian, we analyze spectral fluctuation properties, like Nearest Neighbour Spacing Distribution (NNSD) and Dyson-Mehta (Δ₃) statistic, as a function of λ- the two-body interaction strength. Numerical calculations are used to demonstrate that for very small value of λ, NNSD and Δ₃ are found close to Poisson form and they move steadily to GOE form as λ increases. Moreover, spin dependence of the transition point λ _C is obtained. It is also verified using periodogram analysis that BEGOE(1 + 2)-F spectra shows 1/f–noise behaviour.