We study the formation of topological defects in nonequilibrium phase transitions of both classical and quantum field theory. We examine three model systems. 1). The phase transition of a quantum scalar field in a FRW universe is analyzed through a first-principles approach in which the dynamics of the two-point function is derived from the two-loop, two-particle-irreducible closed-time-path effective action. Identifying signatures of correlated domains in the infrared portion of the momentum-space power spectrum we find that the domain size scales as a power-law with the expansion rate of the universe. The observed power-law scaling is in good agreement with the predictions of the Kibble-Zurek mechanism of defect formation and provides evidence of the freeze-out scenario in the context of nonequilibrium quantum field theory. 2). The formation and interaction of topological textures is analyzed in the phase transition of a classical O(3) scalar field theory in 2+1 dimensions. We provide quantiive arguments that by the end of the transition the length scales of the texture distribution result from a competition between the length scale determined at freeze-out and the ordering dynamics of a textured system. 3). We discuss a black hole phase transition in semiclassical gravity. We review the thermodynamics of a black hole system and determine that the phase transition is entropically driven. We introduce a quantum atomic model of the equilibrium black hole system and show that the phase transition is realized as the abrupt excitation of a high energy state. We investigate the nonequilibrium dynamics of the black hole phase transition and explore similar examples from the Kosterlitz-Thouless transition in condensed matter to the Hagedorn transition in string theory.
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