# Thermalization of overpopulated systems in the 2PI formalism

## TL;DR

This paper investigates how overpopulated scalar systems thermalize using the 2PI formalism, focusing on soft mode growth and transient Bose-Einstein condensate formation, revealing that particle number changing processes prevent BEC formation.

## Contribution

It applies the 2PI formalism to study thermalization in overpopulated systems, highlighting the role of particle number changing processes in preventing BEC formation.

## Key findings

- Rapid approach to condensation threshold
- Particle number changing processes hinder BEC formation
- Soft modes grow significantly during thermalization

## Abstract

Based on the two-particle irreducible (2PI) formalism to next-to-leading order in the $1/N$ expansion, we study the thermalization of overpopulated systems in scalar $O(N)$ theories with moderate coupling. We focus in particular on the growth of soft modes, and examine whether this can lead to the formation of a transient Bose-Einstein condensate (BEC) when the initial occupancy is high enough. For the value of the coupling constant used in our simulations, we find that while the system rapidly approaches the condensation threshold, the formation of a BEC is eventually hindered by particle number changing processes.