The local thermodynamic instability from negative susceptibility in a holographic superfluid with nonlinear terms

TL;DR

This paper investigates local thermodynamic instability in a holographic superfluid model with nonlinear terms, revealing negative susceptibility regions and phase transition behaviors that could inform vortex and turbulence phenomena.

Contribution

It uncovers the negative susceptibility-induced instability and demonstrates how nonlinear terms can refine the phase diagram in holographic superfluids.

Findings

Negative susceptibility indicates local thermodynamic instability.

Nonlinear terms can eliminate complex phase diagram regions.

Different phase transition orders in grand canonical and canonical ensembles.

Abstract

The local thermodynamic stability from the charge susceptibility of a holographic superfluid model at finite superfluid velocity is studied in the probe limit. Previous studies show that beyond a finite value of the superfluid velocity, the superfluid phase transition in the grand canonical ensemble becomes first order. We further reveal that in the canonical ensemble, the superfluid phase transition is still second order, and the difference indicates a section with negative susceptibility which means local thermodynamic instability beyond this superfluid velocity. However, we also meet the ``cave of wind'' behavior at larger superfluid velocity which complicate the phase diagram. We further study the influence of the two nonlinear terms $\lambda|\psi|^4$ and $\tau|\psi|^6$ with parameters $\lambda$ and $\tau$ on the condensate curves, and set appropriate values of $\lambda$ and $\tau$ to remove the "cave of wind" region in the canonical ensemble to get a more elegant phase diagram and better represent the region with such instability, which is possible to be used to realize spontaneous formation of vortexes and quantum turbulence.