Quantum decoherence of subcritical bubble in electroweak phase transition

In a weakly first order phase transition, the typical scale of a subcritical bubble calculated in our previous papers turned out to be too small. At this scale quantum fluctuations may dominate, and our previous classical result may be altered. We thus examine the critical size of a subcritical bubble where a quantum-to-classical transition occur through quantum decoherence. We show that this critical size is almost equal to the typical scale which we obtained previously.