On the Metastability of Quantum Fields in Thermal Bath

TL;DR

This paper studies the metastability of scalar quantum fields at finite temperature, introducing a new numerical method to analyze bounce solutions that describe phase transitions in a thermal environment.

Contribution

A novel numerical approach to determine finite-temperature bounce solutions, distinguishing between $ au$-dependent and $ au$-independent bounces, and analyzing their stability and transition behavior.

Findings

Identified critical temperature where $ au$-independent bounce destabilizes.

Found smooth transition between bounce types in thick-wall scenarios.

Discontinuous transition between bounce types in thin-wall scenarios.

Abstract

We investigate the metastability of scalar fields in quantum field theories at finite temperature, focusing on a detailed understanding of the bounce solution. At finite temperature, the bounce solution depends on two variables: the Euclidean time $\tau$ and the spatial radial distance $r$, and it is periodic in the $\tau$ direction. We propose a novel method to determine the bounce that describes transitions in a thermal bath, suitable for numerical calculations. Two types of bounces exist for transitions in the thermal bath: $\tau$-dependent and $\tau$-independent bounces. We apply our method to compute these bounces in several models, including both thin-wall and thick-wall scenarios, to examine their properties. Specifically, we evaluate the critical temperature below which the $\tau$-independent bounce becomes destabilized due to fluctuations, rendering it irrelevant. We demonstrate that in the thick-wall case, the $\tau$-dependent bounce smoothly transitions into the $\tau$-independent one as temperature increases, whereas in the thin-wall case, the transition between the two types of bounces is discontinuous.