Counterflow and coflow instabilities in miscible binary superfluids

TL;DR

This paper investigates counterflow and coflow instabilities in binary superfluids, deriving a universal instability criterion, verifying it through holographic models and Gross-Pitaevskii simulations, and analyzing the nonlinear evolution of these instabilities.

Contribution

It extends the thermodynamic instability criterion to binary superfluids, verified via holography and weakly interacting models, and explores their nonlinear dynamics.

Findings

Instability onset linked to divergence of the Hessian of free energy.

Universal criterion applies at both finite and zero temperature.

Vortex annihilation restores superfluid stability.

Abstract

We explore instabilities in binary superfluids with a nonvanishing relative superflow, particularly focusing on counterflow and coflow instabilities. We extend recent results on the thermodynamic origin of finite superflow instabilities in single-component superfluids to binary systems and derive a criterion for the onset of instability through a hydrodynamic analysis, which applies to interacting many-body systems at finite temperature. We find that the onset of these instabilities is signaled by the determinant of the Hessian of the thermal free energy diverging and changing sign. We verify this hydrodynamic prediction in a holographic binary superfluid modeled with gauge/gravity duality, which naturally incorporates strong coupling, finite temperature, and dissipation. We also compare to results obtained using the Gross-Pitaevskii equation for weakly interacting Bose-Einstein condensates and find that the same criterion continues to apply at zero temperature, where it reduces to evaluating derivatives of the supercurrents with respect to the superfluid velocities. We observe that the critical velocities of these instabilities follow a general scaling law related to the interaction strength between superfluid components. Finally, the nonlinear stages of the instabilities are studied by full time evolution using gauge/gravity duality, where vortex annihilation leads to a decrease of superfluid velocity back to a value where the binary superfluid phase is stable.