Numerical Aspects of Bubble Nucleation

The effective potential determines the vacuum state of a quantum field theory. When radiative corrections are included or, if one constructs the finite temperature version of field theory the (effective)potential may have two minimum, one of which is lower than the other. The ’higher’ minimum is referred to as the false or metastable vacuum. The global minimum is the true vacuum state of the theory. The existence of these metastable vacua have interesting consequences in the early Universe. If at early times the field settles in the false vacuum it may ’decay’ to the true vacuum either by quantum tunneling or thermal hopping. The transition region is spherically symmetric in coordinate space. Bubbles of the stable phase appear in the metastable phase. In relativistic field theory a formalsim for calculating decay rates from the unstable to the stable vacuum has been developed. Since potentials which are non-linear in the fields are inherent in these problems, it is usually not always possible to find analytic solutions to the decay rate equations. Numerical methods are employed in order to avoid too many analytic approximations. For example, in one detailed numerical study, a scalar field in 1 + 1 dimensions in contact with a thermal bath was modeled using a phenomenological Langevin equation with a field independent, white noise driving term. There have been attempts to derive a Langevin equation containing fluctuation and dissipation terms from purely field theory considerations. In these works the authors considered different models for the thermal bath, but the common result obtained was the possiblity that the thermal noise in the Langevin equation could be colored and depend on the field. In this work we investigate the effects of these non-linear fluctuation and dissipation