Abstract
Numerical simulations of expanding plasma based on the AdS/CFT correspondence as well as kinetic theory and hydrodynamic models strongly suggest that some observables exhibit universal behaviour even when the system is not close to local equilibrium. This leading behaviour is expected to be corrected by transient, exponentially decaying contributions which carry information about the initial state. Focusing on late times, when the system is already in the hydrodynamic regime, we analyse numerical solutions describing expanding plasma of strongly coupled N=4 supersymmetric Yang–Mills theory and identify these transient effects, matching them in a quantitative way to leading transseries corrections corresponding to least-damped quasinormal modes of AdS black branes. In the process we offer additional evidence supporting the recent identification of the Borel sum of the hydrodynamic gradient expansion with the far-from-equilibrium attractor in this system.
Highlights
Given the critical role of hydrodynamics in the physical picture behind the evolution of quark-gluon plasma created in heavy ion collisions, it is very important to have a reliable understanding of how relativistic systems in highly nonequilibrium initial states tend toward local equilibrium
The first is characterised by the quasi-exponential decay of transient effective degrees of freedom – the nonhydrodynamic modes, which in the case of N = 4 supersymmetric Yang-Mills theory (SYM) plasma are in one-to-one correspondence with the quasinormal modes of AdS black branes [1, 2]
It is gratifying that these effects can be found in the precise form expected on the basis of the identification of transient, nonhydrodynamic modes of the expanding plasma with the quasinormal modes of AdS black branes and the realization that the hydrodynamic gradient expansion is the leading element of a transseries
Summary
Given the critical role of hydrodynamics in the physical picture behind the evolution of quark-gluon plasma created in heavy ion collisions, it is very important to have a reliable understanding of how relativistic systems in highly nonequilibrium initial states tend toward local equilibrium. This pattern holds both in microscopic theories and at the level of hydrodynamic models, such as the Muller-Israel-Stewart (MIS) theory [3, 4] and its variants This qualitative picture can be made quantitative and appreciated most clearly when examining certain special observables which enjoy universal behaviour at late times: they evolve (up to exponentially small corrections) in a way determined solely by some microscopic model and independently of the initial conditions. The calculations reported here are aimed at comparing the form of this leading correction with numerical solutions of the full time evolution starting from some randomly chosen initial states Such calculations, based on the AdS/CFT correspondence, were performed in Refs.
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