Oscillating scalar dissipating in a medium

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.

Automated summary

The study investigates the damping effects on the oscillations of a scalar field condensate in a thermal medium caused by dissipative effects. Through multiple-scale perturbation theory, approximate analytical solutions valid for very long times are obtained, revealing power-law damping of oscillations due to non-linear effects. By approximating the non-local equation of motion with a Markovianized one, it is justified to use Markovian equations at leading order, showing that standard time-dependent perturbation theory is insufficient to describe the non-linear condensate evolution. The macroscopic evolution of the condensate is explained in terms of microphysical particle processes.