Note on Zero Temperature Holographic Superfluids

TL;DR

This paper analytically proves the equality of superfluid and particle densities at zero temperature, identifies hydrodynamic modes and sound speed behavior, and demonstrates non-thermalization in holographic superfluids using numerical relativity.

Contribution

It provides an analytic proof of superfluid and particle density equality and combines numerical and analytical methods to study hydrodynamics and non-thermalization in zero temperature holographic superfluids.

Findings

Superfluid density equals particle density at zero temperature.

Sound speed increases with chemical potential and saturates at large values.

Non-thermalization persists in non-linear evolution, supported by a conserved Noether charge.

Abstract

In this note, we have addressed various issues on zero temperature holographic superfluids. First, inspired by our numerical evidence for the equality between the superfluid density and particle density, we provide an elegant analytic proof for this equality by a boost trick. Second, using not only the frequency domain analysis but also the time domain analysis from numerical relativity, we identify the hydrodynamic normal modes and calculate out the sound speed, which is shown to increase with the chemical potential and saturate to the value predicted by the conformal field theory in the large chemical potential limit. Third, the generic non-thermalization is demonstrated by the fully non-linear time evolution from a non-equilibrium state for our zero temperature holographic superfluid. Furthermore, a conserved Noether charge is proposed in support of this behavior.