Dynamical Viscosity of Nucleating Bubbles

TL;DR

This paper investigates how viscosity influences the growth rate of nucleating bubbles during a first order phase transition, providing theoretical estimates and analyzing effects in different dimensions.

Contribution

It introduces a non-equilibrium equation of motion for bubble growth, incorporating viscosity effects from quantum and thermal fluctuations, especially in the thin wall approximation.

Findings

Viscosity corrections depend on fluctuations around the critical bubble.

In 1+1 dimensions, growth rate estimates depend on the free energy functional.

In 3+1 dimensions, surface wave fluctuations lead to leading viscosity corrections.

Abstract

We study the viscosity corrections to the growth rate of nucleating bubbles in a first order phase transition in scalar field theory. We obtain the non-equilibrium equation of motion of the coordinate that describes small departures from the critical bubble and extract the growth rate consistently in weak coupling and in the thin wall limit. Viscosity effects arise from the interaction of this coordinate with the stable quantum and thermal fluctuations around a critical bubble. In the case of 1+1 dimensions we provide an estimate for the growth rate that depends on the details of the free energy functional. In 3+1 dimensions we recognize robust features that are a direct consequence of the thin wall approximation and give the leading viscosity corrections.These are long-wavelength hydrodynamic fluctuations that describe surface waves, quasi-Goldstone modes which are related to ripples on interfaces in phase ordered Ising-like systems. We discuss the applicability of our results to describe the growth rate of hadron bubbles in a quark-hadron first order transition.