From Boltzmann equations to steady wall velocities
  By means of a relativistic microscopic approach we calculate the expansion
velocity of bubbles generated during a first-order electroweak phase
transition. In particular, we use the gradient expansion of the Kadanoff-Baym
equations to set up the fluid system. This turns out to be equivalent to the
one found in the semi-classical approach in the non-relativistic limit.
Finally, by including hydrodynamic deflagration effects and solving the Higgs
equations of motion in the fluid, we determine velocity and thickness of the
bubble walls. Our findings are compared with phenomenological models of wall
velocities. As illustrative examples, we apply these results to three theories
providing first-order phase transitions with a particle content in the thermal
plasma that resembles the Standard Model.
