  Scalar field theory with large infrared initial occupancy develops very large
deep-infrared occupancy, which locally resembles a Bose-Einstein condensate. We
study the structure and spatial coherence of this condensate. The O(N)
symmetric theory with N>1 is qualitatively different than N=1. We explain the
thermodynamical reason why, for N>1, the condensate locally carries nearly
maximal conserved charge density. We also show how this property impedes the
condensate's decay, and we show that it prevents the condensate from ever
becoming fully spatially homogeneous. For N <= 4 the condensate can carry
topological defects, but these do not appear to control the large-k tail in its
power spectrum, which is the same for N=8 where there are no topological
defects.
