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. For a model system, we consider $\mathcal{O}(N)$-symmetric scalar field theories. We use classical-statistical real-time simulations as well as a systematic $1/N$ expansion of the quantum (two-particle-irreducible) 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 $N\ge 2$, 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.

• Received 11 August 2017

DOI:https://doi.org/10.1103/PhysRevD.96.076020