We study the formation of topological defects in nonequilibrium phasetransitions of both classical and quantum field theory. We examine three modelsystems. 1). The phase transition of a quantum scalar field in a FRW universeis analyzed through a first-principles approach in which the dynamics of thetwo-point function is derived from the two-loop, two-particle-irreducibleclosed-time-path effective action. Identifying signatures of correlated domainsin the infrared portion of the momentum-space power spectrum we find that thedomain size scales as a power-law with the expansion rate of the universe. Theobserved power-law scaling is in good agreement with the predictions of theKibble-Zurek mechanism of defect formation and provides evidence of thefreeze-out scenario in the context of nonequilibrium quantum field theory. 2).The formation and interaction of topological textures is analyzed in the phasetransition of a classical O(3) scalar field theory in 2+1 dimensions. Weprovide quantiive arguments that by the end of the transition the length scalesof the texture distribution result from a competition between the length scaledetermined at freeze-out and the ordering dynamics of a textured system. 3). Wediscuss a black hole phase transition in semiclassical gravity. We review thethermodynamics of a black hole system and determine that the phase transitionis entropically driven. We introduce a quantum atomic model of the equilibriumblack hole system and show that the phase transition is realized as the abruptexcitation of a high energy state. We investigate the nonequilibrium dynamicsof the black hole phase transition and explore similar examples from theKosterlitz-Thouless transition in condensed matter to the Hagedorn transitionin string theory.
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