Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme

TL;DR

This paper demonstrates that an interacting quantum field, analyzed using the next-to-leading order large N approximation within the CTP-2PI framework, can exhibit signs of thermalization without an external heat bath.

Contribution

It develops a 2PI effective action approach at NLO in 1/N and shows that solutions to the Schwinger-Dyson equations are inherently thermal, supporting the occurrence of thermalization.

Findings

Only thermal solutions are translation invariant in this approximation.

Thermalization can occur without an external heat bath.

Supports previous numerical evidence of quantum field thermalization.

Abstract

In this paper we use an O(N)-invariant scalar field of unbroken symmetry to investigate whether an interacting quantum field at the next-to-leading order Large $N$ approximation may show signs of thermalization. We develop the closed time-path (CTP) two-particle irreducible (2PI) effective action in powers of 1/N, retaining up to next to leading order (O(1)) terms, and write down the corresponding (truncated) Schwinger-Dyson equations for its two point function. We show that in this approximation, the only translation invariant solutions to the Schwinger - Dyson equations are thermal. This provides a useful temperature concept without invoking a heat bath. When combined with the familiar Kadanoff-Baym approach to quantum kinetic theory our result shows that at this order of approximation thermalization can occur, at least if initial conditions are smooth enough that a derivative expansion is valid. Our analytic result provides support for similar claims in recent literature based on numerical evidence.