Abstract
We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.
Highlights
Takes place in a plasma of produced particles which practically constitute a thermodynamic ensemble described by a von Neumann density operator
Such are the Kadanoff-Baym equations supplemented by the effective condensate equation that arise in the two-particle-irreducible (2PI) effective action formalism that we utilize here
The non-equilibrium and the non-linear nature of the problem necessitates a judicious choice of formalism and approximation methods for describing the evolution
Summary
Constructing the 2PI-resummed effective action requires us to solve for the two-point functions up to quadratic order in the condensate. Since we are interested in the small field expansion of the 2PI-resummed effective action, it suffices to solve for the two-point functions above up to quadratic order. Local diagrams can only be quadratic in the fields, and we truncate them to the leading one-loop order in (2.21b). The kinds of effects that non-local diagrams can induce depend on the power of condensate fields appearing in them. At this order of truncation there is no dependence on the self-coupling λχ of the χ-field This is, not the case as the thermal masse (2.18b) of the corresponding resummed propagator depends on this coupling constant
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