Effective convergence of the two-particle irreducible $1/N$ expansion for nonequilibrium quantum fields

Effective convergence of the two-particle irreducible $1 / N$ expansion for nonequilibrium quantum fields

Gert Aarts, Nathan Laurie, and Anders Tranberg

Phys. Rev. D 78, 125028 – Published 29 December 2008

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.