Condensates in Relativistic Scalar Theories

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.