Nonlinear amplification of instabilities with longitudinal expansion

Abstract

We study the dynamics of nonequilibrium instabilities in anisotropically expanding systems. The most prominent example of such a system is the 'Glasma' in the context of relativistic heavy-ion collision experiments, where the expansion is a consequence of approximately boost-invariant initial conditions. Here we consider the problem of parametric resonance in scalar $N$-component quantum field theories with boost-invariant initial conditions, which is similar in spirit. We find that many aspects of the dynamics can be treated analytically by introducing a generalized conformal time. Primary instabilities, which are described by the linearized evolution equations, are seen to lead to a secondary regime of amplifications with strongly enhanced growth rates due to nonlinear corrections. For the secondary instabilities we present a power-counting scheme for weak coupling, and discuss their role for the question of isotropization and the establishment of an equation of state.Comment: 18 pages, 14 figure

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation, and a challenge for kinetic theory

“…In the following, we will employ the coherent field initial conditions of Eq. (9) for finite values λ 1 and momentum cutoffs only to show that after the parametric time ∼ log 3/2 (λ −1 ) the initial field decays [71] and one recovers the fluctuation initial conditions of Eq. (8).…”

“…(9). These initial conditions lead to a parametric resonance instability at early times in the static case [78][79][80] as well as the expanding scalar field theory [71,77] despite the longitudinal expansion. As shown in Fig.…”

“…Details of the numerical implementation of initial conditions are well documented in the literature [42,70,71] and are summarized in App. A.…”

“…Though small initially, the fluctuations grow exponentially because of an instability [71,77]. Once they become larger than unity, but are still much smaller than the coherent field part, one uses the result as the input for a classicalstatistical description which is fully nonlinear.…”

Parametric instability of classical Yang-Mills fields in a color magnetic background

“…Parametric resonance also might trigger thermalization in heavy-ion collisions because it can give rise to rapid particle production. Instability due to parametric resonance in the O(N) scalar field theory has been analyzed and an exponential growth of the particle number is demonstrated in numerical analyses [30][31][32]. The present analysis should give a general and lucid mathematical basis of the parametric resonance or parametric instability ubiquitous in many fields of physics.…”