Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields

TL;DR

This paper demonstrates that the 1/N expansion of the 2PI effective action converges rapidly for nonequilibrium quantum fields, validated through numerical comparisons in the O(N) model and classical statistical field theory.

Contribution

It provides a detailed numerical analysis showing effective convergence of the 1/N expansion in nonequilibrium quantum field dynamics, including higher-order corrections.

Findings

Rapid convergence observed for moderate 1/N or coupling values

Effective approach for early-time nonequilibrium dynamics

Validation through classical statistical field theory comparisons

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 quasi-particle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling.