  We study the impact of attractive self-interactions on the nonequilibrium
dynamics of relativistic quantum fields with large occupancies at low momenta.
Our primary focus is on Bose-Einstein condensation and nonthermal fixed points
in such systems. As a model system we consider O(N)-symmetric scalar field
theories. We use classical-statistical real-time simulations, as well as a
systematic 1/N expansion of the quantum (2PI) effective action to
next-to-leading order. When the mean self-interactions are repulsive,
condensation occurs as a consequence of a universal inverse particle cascade to
the zero-momentum mode with self-similar scaling behavior. For attractive mean
self-interactions the inverse cascade is absent and the particle annihilation
rate is enhanced compared to the repulsive case, which counteracts the
formation of coherent field configurations. For N >= 2, the presence of a
nonvanishing conserved charge can suppress number changing processes and lead
to the formation of stable localized charge clumps, i.e. Q-balls.
