N-component Bose-Einstein Condensate in an Optical Lattice: Destruction   of the Condensate and Quasiparticle Properties
  We present a model of N-component hard-core bosons on a lattice. The limit N to infinity can be solved exactly. A saddle point approximation leads to a 1/N expansion and allows the calculation of physical quantities like the density of the condensate, the correlation between the components and the density-density correlation function and the correlation between different components. We find a superfluid phase with a tendency towards a Mott insulator at high densities and finite N. 
C. Moseley and K. Ziegler