Relativistic hydrodynamics with phase transition

TL;DR

This paper investigates the limits of hydrodynamic expansions near phase transitions using gauge/gravity duality, revealing that breakdown occurs only at second-order transitions and exploring chaos-related phenomena.

Contribution

It introduces a detailed analysis of hydrodynamic series convergence and chaos behavior across different phase transition types within a holographic model.

Findings

Hydrodynamic series breaks down only at second-order phase transitions.

High- and low-temperature limits of the convergence radius are equal.

Pole-skipping behavior emerges at the chaos point for perturbations.

Abstract

Assessing the applicability of hydrodynamic expansions close to phase transition points is crucial from either theoretical or phenomenological points of view. We explore this within the gauge/gravity duality, using the Einstein-Klein-Gordon model, a bottom-up string theory construction. This model incorporates a parameter, $B_4$, that simulates different types of phase transitions in the strongly coupled field theory existing at the boundary. We thoroughly examine the thermodynamics and dynamics of time-dependent, linearized perturbations in the spin-2, spin-1, and spin-0 sectors. Our findings suggest that "hydrodynamic series breakdown near transition points" is valid exclusively for second-order phase transitions, not for crossovers or first-order phase transitions. Additionally, we observe that the high-temperature and low-temperature limits of the radius of convergence for the hydrodynamic series ($q^2_c$) are equal. We also discover that the relationship $(\text{Max}\vert q^2_c \vert)_{\text{spin-2}} < (\text{Max}\vert q^2_c\vert)_{\text{spin-0}} < (\text{Max}\vert q^2_c \vert)_{\text{spin-1}}$ is consistent for different spin sectors, regardless of the phase transition type. At the chaos point, we observe the emergence of pole-skipping behavior for both gravity and scalar perturbations at $\omega_n = - 2\pi T n i$. Lastly, comparing the chaos momentum with $q^2_c$, we find that $q^2_{ps} < q^2_c$, except for extremely high temperatures.