Oscillating scalar dissipating in a medium

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.

Dissipation of oscillating scalar backgrounds in an FLRW universe

“…In this paper we generalize the work [44] to a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. This generalization is of closer relevance to the perturbative reheating process in the early Universe.…”

“…Important progress has been made recently in Ref. [44] where the authors were able to solve the equation of motion for the scalar condensate analytically in the small-field regime and when the oscillation is quasi-harmonic. 4 A crucial development made in Ref.…”

“…4 A crucial development made in Ref. [44] is introducing the multi-scale analysis [46,47] to solving the non-local equation of motion for the condensate. This method assumes that physical processes happen on different time scales.…”

“…4 For an excellent complementary understanding to Ref. [44], see the recent work [45] where the authors study the condensate evolution beyond the small-field regime and solve the coupled equations of motion for the condensate and two-point functions numerically, capturing effects from both parametric resonance and spinodal instability.…”

“…5 The outline of the paper is as follows. In the next section, we introduce our model and review the derivation of the condensate equation of motion using the two-particle-irreducible (2PI) effective action [44,55]. In Sec.…”