On the dynamics of phase transitions and the nonequilibrium formation of topological defects

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.