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We analyze the structure of eigenstates in many-body bosonic systems bymodeling the Hamiltonian of these complex systems using Bosonic EmbeddedGaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus $k$-bodyrandom interactions. The quantities employed are the number of principalcomponents (NPC), the localization length ($l_H$) and the entropy production$S(t)$. The numerical results are compared with the analytical formulasobtained using random matrices which are based on bivariate $q$-Hermitepolynomials for local density of states $F_k(E|q)$ and the bivariate$q$-Hermite polynomial form for bivariate eigenvalue density$\rho_{biv:q}(E,E_k)$ that are valid in the strong interaction domain. We alsocompare transport efficiency in many-body bosonic systems using BEGOE inabsence and presence of centrosymmetry. It is seen that the centrosymmetryenhances quantum efficiency.

Eigenstate structure in many-body bosonic systems: Analysis using random matrices and $q$-Hermite polynomials