Linearized nonequilibrium dynamics in nonconformal plasma

We investigate the behavior of the lowest nonhydrodynamic modes in a class of holographic models which exhibit an equation of state closely mimicking the one determined from lattice QCD. We calculate the lowest quasinormal mode frequencies for a range of scalar self-interaction potentials and find that the damping of the quasinormal modes at the phase transition/crossover falls off by a factor of around two from conformality after factoring out standard conformal temperature dependence. The damping encoded in the imaginary part of the frequencies turns out to be correlated with the speed of sound and is basically independent of the UV details of the model. We also find that the dynamics of the nonhydrodynamic degrees of freedom remains ultralocal, even to a higher degree, as we deviate from conformality. These results indicate that the role of nonhydrodynamic degrees of freedom in the vicinity of the crossover transition may be enhanced.

Figure 1

The speed of sound $c_s^2$ for the potentials $V_1-V_5$ correspond to deformations of the theory by operators of dimensions 3.93, 3.67, 3.55, 3.10, 3.00 respectively given in Table 1, together with lattice QCD data from [17].

Figure 2

The imaginary parts of the lowest quasinormal mode at $k=0$ for the potentials from Table 1 (left). The imaginary part for potential $V_2$ together with the “phenomenological” according to Eq. (33) (right).

Figure 3

The real part of the lowest quasinormal mode at $k=0$ for the potentials from Table 1 (left) and the ratio of the real to the imaginary part (right).

Figure 4

The curvature at $k=0$ of the damping frequency, overlayed with $\alpha \simeq 1.114$ and $\beta \simeq 0.342$ for the potential $V_2$ in Table 1.

Figure 5

The speed of sound $c_s^2$ (left) and the imaginary parts of the lowest quasinormal modes at $k=0$ (right) for the potentials from Table 2. The one with cusp in the $c_s^2$ (left) corresponds to the most decreased in damping (right).

Figure 6

The curvature at $k=0$ for the damping frequency for potentials from Table 2 (left) and the ratio of the real to the imaginary part (right) for the same potentials.