Holographic Superfluids and the Landau Criterion

TL;DR

This paper investigates the stability of holographic superfluids at finite velocities using quasinormal modes, revealing conditions for instabilities and potential inhomogeneous phases.

Contribution

It applies the Landau criterion to holographic superfluids' quasinormal modes, identifying velocity-dependent instabilities and suggesting possible phase transitions.

Findings

Sound velocity becomes negative at high superfluid velocities.

Instability occurs at finite wavelength, indicating inhomogeneous phases.

Quadratic dispersion modes are unstable at any superfluid velocity.

Abstract

We revisit the question of stability of holographic superfluids with finite superfluid velocity. Our method is based on applying the Landau criterion to the Quasinormal Mode (QNM) spectrum. In particular we study the QNMs related to the Goldstone modes of spontaneous symmetry breaking with linear and quadratic dispersions.In the linear case we show that the sound velocity becomes negative for large enough superfluid velocity and that the imaginary part of the quasinormal frequency moves to the upper half plane. Since the instability is strongest at finite wavelength, we take this as an indication for the existence of an inhomogeneous or striped condensed phase for large superfluid velocity. In the quadratic case the instability is present for arbitrarily small superfluid velocity.