General bubble expansion at strong coupling

TL;DR

This paper extends analytical relations between pressure differences and bubble wall velocities in strongly coupled first-order phase transitions to more realistic equations of state, aiding future holographic numerical simulations.

Contribution

It generalizes previous analytic relations to realistic equations of state beyond the bag model for strongly coupled phase transitions.

Findings

Linear correlation between phase pressure difference and wall velocity.

Quadratic correlation between wall pressure difference and wall velocity.

Most general predictions for holographic simulations of phase transitions.

Abstract

The strongly coupled system like the quark-hadron transition (if it is of first order) is becoming an active play yard for the physics of cosmological first-order phase transitions. However, the traditional field theoretic approach to strongly coupled first-order phase transitions is of great challenge, driving recent efforts from holographic dual theories with explicit numerical simulations. These holographic numerical simulations have revealed an intriguing linear correlation between the phase pressure difference (pressure difference away from the wall) to the nonrelativistic terminal velocity of an expanding planar wall, which has been reproduced analytically alongside both cylindrical and spherical walls from perfect-fluid hydrodynamics in our previous study but only for a bag equation of state. We also found, in our previous study, a universal quadratic correlation between the wall pressure difference (pressure difference near the bubble wall) to the nonrelativistic terminal wall velocity regardless of wall geometries. In this paper, we will generalize these analytic relations between the phase/wall pressure difference and terminal wall velocity into a more realistic equation of state beyond the simple bag model, providing the most general predictions so far for future tests from holographic numerical simulations of strongly coupled first-order phase transitions