On the hydrodynamic attractor of Yang–Mills plasma

Abstract

There is mounting evidence suggesting that relativistic hydrodynamics becomes relevant for the physics of quark-gluon plasma as the result of nonhydrodynamic modes decaying to an attractor apparent even when the system is far from local equilibrium. Here we determine this attractor for Bjorken flow in N = 4 supersymmetric Yang-Mills theory (SYM) using Borel summation of the gradient expansion of the expectation value of the energy momentum tensor. By comparing the result to numerical simulations of the flow based on the AdS/CFT correspondence we show that it provides an accurate and unambiguous approximation of the hydrodynamic attractor in this system. This development has important implications for the formulation of effective theories of hydrodynamics.

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

“…When the width of the bands is small, we can use the resummation to explore the process of hydrodynamization of the system. As already observed in [36] for N = 4, the result of these resummations quickly approaches the first order hydrodynamic predictions for all the values of λ GB . To better quantify this process, we will assume that the system has hydrodynamized at w hyd if for any larger value of w the anisotropy function satisfies where R hyd is the first order hydrodynamic expression eq.…”

“…cos(an)), in a similar fashion to scenarios noted in [28,36]. As we vary λ GB to decreasing values we find that the oscillating behaviour becomes suppressed and the coefficients tend to follow r n ∼ n!…”

“…As λ GB becomes more negative, the value of the temperature-normalised gradient w at which hydrodynamization occurs increases, as expected by the fact that the dual fluid is more viscous. Nevertheless, as in other theories where the resummation has been performed [26,36], R hyd approximates the resummed result even when the value of this normalised gradient is comparable to the microscopic scale. At these small values of the inverse gradient, the anisotropy function is larger than 1, which means that the viscous contribution to the pressures is as large as the equilibrium pressure, demonstrating that the contribution of higher order terms is potentially large.…”

“…We close this section by noticing that the RTA computation exhibits a much stronger dependence on initial conditions that the holographic computations. 8 For RTA not only our estimated hydrodynamization time occurs much later than for the holographic computations, but also at this larger value of the re-scaled gradient the spread of initial conditions is large and many of the individual initial conditions are not well approximated by first 7 We have checked that this procedure leads to a spread in anisotropy paramater comparable to that induced by the different initial conditions in N = 4 SYM reported in [36]. 8 We thank M. Heller, M. Spaliński and V. Svensson for private communication on recent analysis of RTA kinetic theory with a non-conformal relaxation time [75] which exhibits a trans-series structure with multiple independent contributions with identical exponential suppressions.…”

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

“…A more detailed mathematical analysis of the origin of this divergence has unveiled the existence of a unique universal solution, the so-called attractor [25]. The attractor "solution" is intrinsically related to the mathematical theory of resurgence [20,26,27] and its details depend on the particular theory under consideration [28][29][30][31][32][33][34][35][36][37]. In simple terms, the attractor is a set of points in the phase space of the dynamical variables to which a family of solutions of an evolution equation merge after transients have died out.…”