  Bose-Einstein condensation (BEC) of composite diquarks in quark matter (the
color superconductor phase) is discussed using the quasi-chemical equilibrium
theory at a relatively low density region near the deconfinement phase
transition, where dynamical quark-pair fluctuations are assumed to be described
as bosonic degrees of freedom (diquarks). A general formulation is given for
the diquark formation and particle-antiparticle pair-creation processes in the
relativistic flamework, and some interesting properties are shown, which are
characteristic for the relativistic many-body system. Behaviors of transition
temperature and phase diagram of the quark-diquark matter are generally
presented in model parameter space, and their asymptotic behaviors are also
discussed. As an application to the color superconductivity, the transition
temperatures and the quark and diquark density profiles are calculated in case
with constituent/current quarks, where the diquark is in bound/resonant state.
We obtained $T_C \sim 60-80$ MeV for constituent quarks and $T_C \sim 130$ MeV
for current quarks at a moderate density ($\rho_b \sim 3 \rho_0$). The method
is also developed to include interdiquark interactions into the quasi-chemical
equilibrium theory within a mean-field approximation, and it is found that a
possible repulsive diquark-diquark interaction lowers the transition
temperature by nearly 50%.
