  We review the properties of chaoticity and coherence in Bose-Einstein
condensation and correlations, for a dense boson system in its mean-field
represented approximately by a harmonic oscillator potential. The order
parameter and the nature of the phase transition from the chaotic to the
condensate states are studied for different fixed numbers of bosons. The
two-particle correlation function in momentum space is calculated to
investigate how the Bose-Einstein correlation depends on the degree of
condensation and other momentum variables. We generalize the Bose-Einstein
correlation analysis to three-particle correlations to show its dependence on
the degree of condensation.
