Effective convergence of the two-particle irreducible1/Nexpansion for nonequilibrium quantum fields

Abstract

The $1/N$ expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the $1/N$ expansion in the $O(N)$ model by comparing results obtained numerically in $1+1$ dimensions at leading, next-to-leading and next-to-next-to-leading order in $1/N$ as well as in the weak coupling limit. A comparison in classical statistical field theory, where exact numerical results are available, is made as well. We focus on early-time dynamics and quasiparticle properties far from equilibrium and observe rapid effective convergence already for moderate values of $1/N$ or the coupling.