DYNAMICS OF SUBCRITICAL BUBBLES IN FIRST-ORDER PHASE-TRANSITION

We derivate the Langevin and the Fokker-Planck equations for the radiu s of O(3)-symmetric subcritical bubbles as a phenomenological model to treat thermal fluctuation. The effect of thermal noise on subcritical bubbles is examined. We find that the fluctuation-dissipation relatio n holds and that in the high temperature phase the system settles down rapidly to the thermal equilibrium state even if it was in a nonequil ibrium state initially. We then estimate the typical size of subcritic al bubbles as well as the amplitude of fluctuations on that scale. We also discuss their implication to the electroweak phase transition.