  Based on the two-particle irreducible (2PI) formalism to next-to-leading
order in the $1/N$ expansion, we study the thermalization of overpopulated
systems in scalar $O(N)$ theories with moderate coupling. We focus in
particular on the growth of soft modes, and examine whether this can lead to
the formation of a transient Bose-Einstein condensate (BEC) when the initial
occupancy is high enough. For the value of the coupling constant used in our
simulations, we find that while the system rapidly approaches the condensation
threshold, the formation of a BEC is eventually hindered by particle number
changing processes.
