Boost-invariant superfluid flows

TL;DR

This paper derives exact and approximate solutions for relativistic superfluid flows that are invariant under Lorentz boosts, extending classical flow models and analyzing effects of viscosity and symmetry breaking.

Contribution

It introduces superfluid generalizations of Bjorken and Gubser flows, including viscous corrections and effects of explicit symmetry breaking.

Findings

Exact boost-invariant superfluid flow solutions derived.

Viscous corrections dominated by shear viscosity analyzed.

Small symmetry-breaking effects still allow approximate solutions.

Abstract

We present some exact solutions to the ideal hydrodynamics of a relativistic superfluid with an almost-conformal equation of state. The solutions have stress tensors which are invariant under Lorentz boosts in one direction, and represent superfluid generalisations of the Bjorken and Gubser flows. We also study corrections to the flows in first-order hydrodynamics, arguing that dissipation is dominated by the shear viscosity. We present some simple numerical solutions for these viscous corrections. Finally, we estimate the size of corrections to the flows arising when the spontaneously broken $\mathrm{U}(1)$ symmetry responsible for superfluidity is only approximate, giving the corresponding Goldstone boson a small non-zero mass. We find that the massless solutions can still provide good approximations at sufficiently small spatial rapidities.