Critical behavior of non-hydrodynamic quasinormal modes in a strongly coupled plasma

TL;DR

This paper investigates the behavior of non-hydrodynamic quasinormal modes in a strongly coupled plasma near a critical point, revealing how equilibration times and damping rates change with chemical potential and identifying a new purely imaginary mode.

Contribution

It provides a detailed analysis of quasinormal mode spectra near criticality in a holographic model, highlighting novel behaviors of equilibration times and discovering a new purely imaginary mode.

Findings

Equilibration times increase near the critical point but remain finite.

Divergence of the derivative of equilibration time with respect to chemical potential at criticality.

Discovery of a purely imaginary non-hydrodynamical mode in the vector channel.

Abstract

We study the behavior of quasinormal modes in a top-down holographic dual corresponding to a strongly coupled $\mathcal{N} = 4$ super Yang-Mills plasma charged under a $U(1)$ subgroup of the global $SU(4)$ R-symmetry. In particular, we analyze the spectra of quasinormal modes in the external scalar and vector diffusion channels near the critical point and obtain the behavior of the characteristic equilibration times of the plasma as the system evolves towards the critical point of its phase diagram. Except close to the critical point, we observe that by increasing the chemical potential one generally increases the damping rate of the quasinormal modes, which leads to a reduction of the characteristic equilibration times in the dual strongly coupled plasma. However, as one approaches the critical point the typical equilibration time (as estimated from the lowest non-hydrodynamic quasinormal mode frequency) increases, although remaining finite, while its derivative with respect to the chemical potential diverges with exponent -1/2. We also find a purely imaginary non-hydrodynamical mode in the vector diffusion channel at nonzero chemical potential which dictates the equilibration time in this channel near the critical point.