Instabilities in relativistic two-component (super)fluids

TL;DR

This paper investigates the stability and sound modes of relativistic two-component superfluids and normal fluids, revealing conditions under which various instabilities, including two-stream instabilities, occur in different regimes.

Contribution

It provides a systematic analysis of instabilities in relativistic two-fluid systems using a microscopic field-theoretical model, highlighting differences between superfluid and normal fluid cases.

Findings

Two-stream instability in superfluids occurs only beyond Landau's critical velocity.

Transverse modes in normal fluids can become unstable in an energetically stable regime due to entrainment.

Results are applicable to neutron star superfluids and non-relativistic laboratory fluids.

Abstract

We study two-fluid systems with nonzero fluid velocities and compute their sound modes, which indicate various instabilities. For the case of two zero-temperature superfluids we employ a microscopic field-theoretical model of two coupled bosonic fields, including an entrainment coupling and a non-entrainment coupling. We analyse the onset of the various instabilities systematically and point out that the dynamical two-stream instability can only occur beyond Landau's critical velocity, i.e., in an already energetically unstable regime. A qualitative difference is found for the case of two normal fluids, where certain transverse modes suffer a two-stream instability in an energetically stable regime if there is entrainment between the fluids. Since we work in a fully relativistic setup, our results are very general and of potential relevance for (super)fluids in neutron stars and, in the non-relativistic limit of our results, in the laboratory.