Phase Equilibration and Magnetic Field Generation in U(1) Bubble Collisions

TL;DR

This paper investigates the dynamics of bubble collisions in a first-order phase transition within the Abelian Higgs model, deriving analytical solutions and comparing them with numerical results, with implications for primordial magnetic field generation.

Contribution

It introduces new analytical solutions for the Abelian field and phase during bubble collisions, validated against lattice computations, and discusses extensions to electroweak transitions.

Findings

Analytical solutions agree well with numerical simulations for small phase differences.

Closed-form solutions are derived using a step-function approximation.

Potential implications for primordial magnetic field generation are discussed.

Abstract

We present the results of lattice computations of collisions of two expanding bubbles of true vacuum in the Abelian Higgs model with a first-order phase transition. New time-dependent analytical solutions for the Abelian field strength and the phase of the complex field are derived from initial conditions inferred from linear superposition and are shown to be in excellent agreement with the numerical solutions especially for the case where the initial phase difference between the bubbles is small. With a step-function approximation for the initial phase of the complex field, solutions for the Abelian field strength and other gauge-invariant quantities are obtained in closed form. Possible extensions of the solution to the case of the electroweak phase transition and the generation of primordial magnetic fields are briefly discussed.