Hydrodynamics and beyond in the strongly coupled N=4 plasma

TL;DR

This paper investigates the behavior of quasinormal modes in the strongly coupled N=4 plasma, revealing how their residues evolve at short wavelengths and confirming causality, with implications for hydrodynamic scales.

Contribution

It provides a numerical analysis of quasinormal mode residues, showing their behavior at different wavelengths and clarifying the relation between hydrodynamic and higher modes in the plasma.

Findings

Diffusion mode residues decay into damped oscillations at short wavelengths.

Sound mode residues do not decay and resemble higher modes at short wavelengths.

All quasinormal modes, including hydrodynamic ones, obey causality.

Abstract

We continue our investigations on the relation between hydrodynamic and higher quasinormal modes in the AdS black hole background started in arXiv:0710.4458 [hep-th]. As is well known, the quasinormal modes can be interpreted as the poles of the retarded Green functions of the dual N=4 gauge theory at finite temperature. The response to a generic perturbation is determined by the residues of the poles. We compute these residues numerically for energy-momentum and R-charge correlators. We find that the diffusion modes behave in a similar way: at small wavelengths the residues go over into a form of a damped oscillation and therefore these modes decouple at short distances. The sound mode behaves differently: its residue does not decay and at short wavelengths this mode behaves as the higher quasinormal modes. Applications of our findings include the definition of hydrodynamic length and time scales. We also show that the quasinormal modes, including the hydrodynamic diffusion modes, obey causality.