Bubble nucleation around heterogeneities in $\phi^4$-field theories

TL;DR

This paper introduces an exactly solvable $$ model demonstrating bubble nucleation around heterogeneities, revealing complex dynamics and stability properties, supported by numerical simulations.

Contribution

It presents a novel, exactly solvable $$ model for bubble nucleation around heterogeneities, with detailed stability analysis and numerical validation.

Findings

Bubbles exhibit rich dynamical behaviors depending on heterogeneity topology.

Linear stability analysis predicts oscillating and nested bubble formations.

Numerical simulations confirm theoretical predictions in 2+1 dimensions.

Abstract

Localised heterogeneities have been recently discovered to act as bubble-nucleation sites in nonlinear field theories. Vacuum decay seeded by black holes is one of the most remarkable applications. This article proposes a simple and exactly solvable $\phi^4$ model exhibiting bubble nucleation around localised heterogeneities. Bubbles with a rich dynamical behaviour are observed depending on the topological properties of the heterogeneity. The linear stability analysis of soliton-bubbles predicts the formation of oscillating bubbles and the insertion of new bubbles inside an expanding precursor bubble. Numerical simulations in 2+1 dimensions are in good agreement with theoretical predictions.