The characteristics of thermalization of boost-invariant plasma from holography

TL;DR

A sizable anisotropy in the energy-momentum tensor at thermalization is observed, which suggests that effective thermalization in heavy-ion collisions may occur significantly earlier than true thermalization.

Abstract

We report on the approach towards the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at tau=0. The results are obtained through numerical solution of Einstein's equations for the dual geometries, as described in detail in the companion article arXiv:1203.0755. Despite the very rich far-from-equilibrium evolution, we find surprising regularities in the form of clear correlations between initial entropy and total produced entropy, as well as between initial entropy and the temperature at thermalization, understood as the transition to a hydrodynamic description. For 29 different initial conditions that we consider, hydrodynamics turns out to be definitely applicable for proper times larger than 0.7 in units of inverse temperature at thermalization. We observe a sizable anisotropy in the energy-momentum tensor at thermalization, which is nevertheless entirely due to hydrodynamic effects. This suggests that effective thermalization in heavy ion collisions may occur significantly earlier than true thermalization.

Figures (5)

• Figure 1: a) $F(w)/w$ versus $w$ for all 29 initial data. b) Pressure anisotropy $1-\frac{3p_L}{\varepsilon}$ for a selected profile. Red, blue and green curves represent $1^{st}$, $2^{nd}$ and $3^{rd}$ order hydrodynamics fit.
• Figure 2: The apparent horizon (black u-shaped curve) and a radial null geodesic (red curve) sent from the boundary (left edge of the plot) at $\tau=0$ into the bulk for a sample profile.
• Figure 3: Entropy production as a function of initial entropy.
• Figure 4: The dimensionless parameter $w=\tau \, T_{eff}$ at thermalization as a function of the initial entropy $s_{n-eq}^{(i)}$. The straight line corresponds to $w^{(th)} = 0.7$.
• Figure 5: The thermalization time in the units of initial effective temperature (left) and the ratio of thermalization and initial effective temperatures $T_{eff}^{(th)}/T_{eff}^{(i)}$ (right) as functions of the initial entropy $s_{n-eq}^{(i)}$.