We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus
k-body random interactions. The quantities employed are the number of principal components (NPC), the localization length (
lH) and the entropy production
S(t). The numerical results are compared with the analytical formulas obtained using random matrices which are based on bivariate
q-Hermite polynomials for local density of states
Fk(E∣q) and the bivariate
q-Hermite polynomial form for bivariate eigenvalue density
ρbiv:q(E,Ek) that are valid in the strong interaction domain. We also compare transport efficiency in many-body bosonic systems using BEGOE in absence and presence of centrosymmetry. It is seen that the centrosymmetry enhances quantum efficiency.