Homogeneous isotropization and equilibration of a strongly coupled plasma with a critical point

Abstract

Abstract:We use holography to investigate the process of homogeneous isotropization and thermalization in a strongly coupled N = 4 Super Yang-Mills plasma charged under a U(1) subgroup of the global SU(4) R-symmetry which features a critical point in its phase diagram. Isotropization dynamics at late times is affected by the critical point in agreement with the behavior of the characteristic relaxation time extracted from the analysis of the lowest non-hydrodynamic quasinormal mode in the SO(3) quintuplet (external scalar) channel of the theory. In particular, the isotropization time may decrease or increase as the chemical potential increases depending on whether one is far or close enough to the critical point, respectively. On the other hand, the thermalization time associated with the equilibration of the scalar condensate, which happens only after the system has relaxed to a (nearly) isotropic state, is found to always increase with chemical potential in agreement with the characteristic relaxation time associated to the lowest non-hydrodynamic quasinormal mode in the SO(3) singlet (dilaton) channel. These conclusions about the late dynamics of the system are robust in the sense that they hold for different initial conditions seeding the time evolution of the far-from-equilibrium plasma.

Criticality of QCD in a holographic QCD model with critical end point

“…Many efforts have been made in building a realistic holographic QCD model to describe hadron physics , hot/dense QCD matter [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], and so on. For near critical point physics in bottom-up holographic QCD, several groups have developed different models with CEP in the Einstein-Maxwell-Dilaton system [76][77][78][79][80]. The static critical scaling near the CEP is investigated in [77], and it is shown to be α = 0, β ≈ 0.482, γ ≈ 0.942, δ ≈ 3.035, very close to the mean field results.…”

“…The static critical scaling near the CEP is investigated in [77], and it is shown to be α = 0, β ≈ 0.482, γ ≈ 0.942, δ ≈ 3.035, very close to the mean field results. Meanwhile, the dynamical critical exponents, which are related to dynamical evolution of the system towards the critical point, are analyzed in [78][79][80]. Besides, the critical exponents at chiral critical lines are given in [81].…”

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

“…This list may include an investigation of hydrodynamization processes and the dynamics of attractors for more general nonlinear collisional kernels [7,22,90], holographic models [8,[14][15][16][17][18], spatially nonhomogeneous expanding fluids [39] and nonrelativistic systems [51,52]. On the other hand, it is also interesting to investigate the rich structure and topology of the basin of attractors in turbulent flows and other chaotic systems of interest.…”

“…This set defines the basin of attraction: given an initial time τ 0 , there is an associated Tðτ 0 Þ andπðτ 0 Þ, and the basin of attraction is elaborated as the set of all pairs of ðTðτ 0 Þ;πðτ 0 ÞÞ such that the Bjorken flow lines are doomed to limit to the equilibrium. We recall that ðT;πÞ is the actual phase space 8 of the Bjorken flow which fixes the dimensionality of the basin of attraction as well.…”

“…This does not affect the dimensionality of the attractor and hence Gubser flow lines still evolve into a 1-manifold but in reality it is no longer a planar curve since the time direction is not fully decoupled from the ODE in terms of the new time w, which will be 7 Throughout this paper the word "equilibrium" is always meant to be thermal equilibrium and a steady state expresses a state of the system which requires energy or continual work to remain stationary and it thus does not imply thermal equilibrium. 8 In this section, "phase space" is referred to as the space of independent macroscopic variables labeling a flow diagram. The latter represents the dynamics of the underlying hydrodynamical system via the connection between the velocity fields and the macroscopic variables that form the flow lines.…”