Nonequilibrium two-particle irreducible evolution of theO(N)model with longitudinal expansion

Abstract

Motivated by the problem of thermalization in heavy-ion collisions, we present numerical simulations of the nonequilibrium evolution of the O(N) model in 1+2 dimensions with longitudinal expansion and in the presence of a background field. We work in the NLO approximation of the 1/N expansion and consider both the strong and weak coupling cases. Special emphasis is put on the difference between the 2PI formalism and the classical statistical approach. In the 2PI case at strong coupling, we find some evidence of the Bose-Einstein (exponential) distribution in the expanding system.

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

“…(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.…”

“…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.…”

“…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. The whole procedure has a well defined continuum limit such that one gets the physical quantum result [17,72,77]. In the following, we will employ the coherent field initial conditions of Eq.…”

Thermalization of overpopulated systems in the 2PI formalism

“…The BEC formation in the presence of longitudinal expansion has been studied in [25,26] in different approaches. The NLO-2PI simulation in the longitudinally expanding geometry was performed in [20] but in 1+2 dimensions (see also [22]). It should be straightforward to generalize the work of [20] to 1+3 dimensions.…”

“…Unfortunately, in practice, these calculations involve heavy numerics. As a result simulations have been sparse in the literature, often done in 1+1 or 1+2 dimensions [16,17,19,20], and in 1+3 dimensions on small lattices [21,22]. Very recently, a large volume simulation in 1+3 dimensions has appeared [23], but the focus there was on the so-called non-thermal fixed points and the self-similar behaviours which emerge far-from-equilibrium at small coupling.…”