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Dynamics of Phase Transitions Induced by a Heat Bath

We study the non-equilibrium dynamics of a symmetry restoring phase transition in a scalar field theory, the ``system'', linearly coupled to another scalar field taken as a ``heat bath''. The ``system'' is initially in an ordered low temperature phase, and the heat bath is at a temperature close to the critical temperature for the system. We estimate the time at which the phase transition to the disordered (symmetric) phase takes place. We derive, and integrate the one-loop effective equations of motion for the order parameter that include the effects of the heat bath. A semiclassical Langevin equation is derived and it is found that it contains a non-dissipative, non-Markovian kernel, the noise term is colored and correlated on time scales determined by the temperature of the heat bath. The range of validity of the Langevin equation and a consistent procedure to incorporate corrections are discussed.