| The processes by which nonlinear physical systems approach thermal equilibrium is of great importance in many areas of science. Central to this is the mechanism by which energy is transferred between the many degrees of freedom comprising these systems. With this in mind, in this research the nonequilibrium dynamics of nonperturbative fluctuations within Ginzburg-Landau models are investigated. In particular, two questions are addressed. In both cases the system is initially prepared in one of two minima of a double-well potential. First, within the context of a (2 + 1) dimensional field theory, we investigate whether emergent spatio-temporal coherent structures play a dynamcal role in the equilibration of the field. We find that the answer is sensitive to the initial temperature of the system. At low initial temperatures, the dynamics are well approximated with a time-dependent mean-field theory. For higher temperatures, the strong nonlinear coupling between the modes in the field does give rise to the synchronized emergence of coherent spatio-temporal configurations, identified with oscillons. These are long-lived coherent field configurations characterized by their persistent oscillatory behavior at their core. This initial global emergence is seen to be a consequence of resonant behavior in the long wavelength modes in the system.; A second question concerns the emergence of disorder in a highly viscous system modeled by a (3 + 1) dimensional field theory. An integro-differential Boltzmann equation is derived to model the thermal nucleation of precursors of one phase within the homogeneous background. The fraction of the volume populated by these precursors is computed as a function of temperature. This model is capable of describing the onset of percolation, characterizing the approach to criticality (i.e. disorder). It also provides a nonperturbative correction to the critical temperature based on the nonequilibrium dynamics of the system. |
