Bose-Fermi mixed condensates of atomic gas with Boson-Fermion quasi-bound state

The phase structures of the boson-fermion (B and F) mixed condensates of atomic gas are discussed under the existence of boson-fermion composite fermions (quasi-bound states) BF from the equilibrium in B+F -> BF. Especially we discuss the competitions between the BF degenerate states and the Bose-Einstein condensates (BEC) in low-T. The criterion for the BEC realization is obtained from the algebraically-derived phase diagrams at T=0.