Nonhydrodynamic quasinormal modes and equilibration of a baryon dense holographic QGP with a critical point

We compute the homogeneous limit of nonhydrodynamic quasinormal modes (QNMs) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD) holographic model for the quark-gluon plasma (QGP) that is able to i) quantitatively describe state-of-the-art lattice results for the QCD equation of state and higher-order baryon susceptibilities with $2+1$ flavors and physical quark masses up to the highest values of the baryon chemical potential currently reached in lattice simulations, ii) describe the nearly perfect fluidity of the strongly coupled QGP produced in ultrarelativistic heavy-ion collisions, and iii) give a very good description of the bulk viscosity extracted via some recent Bayesian analyses of hydrodynamical descriptions of heavy-ion experimental data. This EMD model has been recently used to predict the location of the QCD critical point in the QCD phase diagram, which was found to be within the reach of upcoming low-energy heavy-ion collisions. The lowest quasinormal modes of the $SO(3)$ rotationally invariant quintuplet, triplet, and singlet channels evaluated in the present work provide upper bounds for characteristic equilibration times describing how fast the dense medium returns to thermal equilibrium after being subjected to small disturbances. We find that the equilibration times in the different channels approach each other at high temperatures, but they are well separated at the critical point. Moreover, in most cases, these equilibration times decrease with increasing baryon chemical potential while keeping the temperature fixed.

Figure 1

Sixth- and eighth-order dimensionless baryon susceptibilities ${\chi }_n\equiv {\partial }^n(P/T^4)/\partial ({\mu }_B/T{)}^n$ predicted by the EMD model in Ref. [24] compared to the very recent lattice QCD results from Ref. [62].

Figure 2

Absolute value of the real part of the lowest QNM in the $SO(3)$ quintuplet channel (top left), the imaginary part of the lowest QNM (top right), the dimensionless combination given by the temperature times the equilibration time (bottom left), and the equilibration time measured in units of fm/$c$ (bottom right) as functions of temperature for different values of the baryon chemical potential. In the upper panels we plot both the calculated points and the interpolated curves between them.

Figure 3

Absolute value of the real part of the lowest QNM in the $SO(3)$ triplet channel (top left), the imaginary part of the lowest QNM (top right), the dimensionless combination given by the temperature times the equilibration time (bottom left), and the equilibration time measured in units of $\mathrm{fm}/c$ (bottom right) as functions of temperature for different values of the baryon chemical potential. In the upper panels we plot both the calculated points and the interpolated curves between them.

Figure 4

In the upper panels we zoom in on the region containing the crossing point for the equilibration time in the $SO(3)$ triplet channel. In the bottom panel we plot the result for the baryon DC conductivity, which also displays a crossing point (although at a lower temperature).

Figure 5

Absolute value of the real part of the lowest QNM in the $SO(3)$ singlet channel (top left), the imaginary part of the lowest QNM (top right), the dimensionless combination given by the temperature times the equilibration time (bottom left), and the equilibration time measured in units of fm/$c$ (bottom right) as functions of temperature for different values of the baryon chemical potential. In the upper panels we plot both the calculated points and the interpolated curves between them.

Figure 6

Grid of backgrounds generated in the plane of initial conditions (left) and in the $(T,{\mu }_B)$ plane (right). The background corresponding to the critical point in the phase diagram is highlighted by the red circle in both panels.