Nonequilibrium Dynamics and Phase Transitions in Holographic Models

We study the poles of the retarded Green’s functions of strongly coupled field theories exhibiting a variety of phase structures from a crossover up to a first order phase transition. These theories are modeled by a dual gravitational description. The poles of the holographic Green’s functions appear at the frequencies of the quasinormal modes of the dual black hole background. We establish that near the transition, in all cases considered, the applicability of a hydrodynamic description breaks down already at lower momenta than in the conformal case. We establish the appearance of the spinodal region in the case of the first order phase transition at temperatures for which the speed of sound squared is negative. An estimate of the preferential scale attained by the unstable modes is also given. We additionally observe a novel diffusive regime for sound modes for a range of wavelengths.

Figure 1

Left panel: equation of state for $V_{1\text{st}}$ potential with different regions marked. The meeting point of red and green lines defines the corresponding minimal temperature $T_m$. Right panel: equation of state for $V_{2\text{nd}}$.

Figure 2

Quasinormal modes for the potential $V_{2\text{nd}}$ at $T_c$: real part (upper panel) and imaginary part (lower panel). The speed of sound and the ratio of bulk viscosity to the entropy density are calculated, namely, $c_s\simeq 0$, $\zeta /s\simeq 0.061$ (cf. [14]).

Figure 3

Sound channel quasinormal modes for the potential $V_{1\text{st}}$ at $T\simeq 1.067T_m\gtrsim T_c$ in the unstable region of the EoS. An instability of the spinodal region is shown in the inset.

Figure 4

Quasinormal modes for the potential $V_{1\text{st}}$ at $T\simeq 1.00004T_m$ in the stable region of the EoS, below the transition $T<T_c\simeq 1.05T_m$: real part (upper panel) and imaginary part (lower panel).