Hydrodynamics and instabilities of relativistic superfluids at finite superflow

TL;DR

This paper investigates the stability of relativistic superfluids with finite superflow, identifying a thermodynamic instability criterion and confirming its applicability through holographic duality and transport coefficient analysis.

Contribution

It introduces a thermodynamic instability criterion for relativistic superfluids with superflow and demonstrates its validity via holographic duality and transport coefficient calculations.

Findings

Instability occurs when bla(n_s) = 0, indicating a divergence in susceptibility.

The instability criterion applies to both relativistic and non-relativistic superfluids.

Holographic computations confirm the matching of quasinormal modes with superfluid hydrodynamics.

Abstract

We study the linear response of relativistic superfluids with a non-zero superfluid velocity. For sufficiently large superflow, an instability develops via the crossing of a pole of the retarded Green's functions to the upper half complex frequency plane. We show that this is caused by a local thermodynamic instability, i.e. when an eigenvalue of the static susceptibility matrix (the second derivatives of the free energy) diverges and changes sign. The onset of the instability occurs when $\partial_{\zeta}(n_s\zeta)=0$, with $\zeta$ the norm of the superfluid velocity and $n_s$ the superfluid density. The Landau instability for non-relativistic superfluids such as Helium 4 also coincides with the non-relativistic version of this criterion. We then turn to gauge/gravity duality and show that this thermodynamic instability criterion applies equally well to strongly-coupled superfluids. In passing, we compute holographically a number of transport coefficients parametrizing deviations out-of-equilibrium in the hydrodynamic regime and demonstrate that the gapless quasinormal modes of the dual planar black hole match those predicted by superfluid hydrodynamics.