Oscillating scalar dissipating in a medium

TL;DR

This paper analyzes the damping of oscillating scalar fields in a thermal medium using non-linear, non-local equations derived from quantum field theory, providing long-time analytic solutions and justifying Markovian approximations.

Contribution

It introduces a novel approach to solve non-local condensate equations with multiple-scale perturbation theory and compares Markovian and non-Markovian models for scalar field damping.

Findings

Power-law damping transitions to exponential damping at late times.

Markovian approximation accurately captures leading-order evolution.

Standard perturbation theory fails beyond early damping stages.

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.