FLUCTUATION-DISSIPATION FORMULA FOR BUBBLE-WALL VELOCITY

We derive a general relation between the steady bubble-wall velocity set by friction effects at a first-order phase transition in a theory with a slightly nondegenerate potential, and an equilibrium correlation function in a theory where the potential is strictly degenerate. The correlation function is expressed through the imaginary, dissipative part of the equilibrium self-energy of the order parameter (a scalar field). We present a sample calculation in a model where parameters were chosen to justify the perturbative evaluation of the self-energy. Our estimate for the electroweak phase transition suggests that, if this transition is of first order, the bubble wall propagates at a nonrelativistic velocity.