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 λthe 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 λC is obtained. It is also verified using periodogram analysis that BEGOE(1 + 2)-F spectra shows 1/f–noise behaviour.