Boost-invariant superfluid flows

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.

22 pages + bibliography, 7 figure files

References in corpus (6)

• The equation of state in (2+1)-flavor QCD
• Holographic model of superfluidity
• A holographic model of deconfinement and chiral symmetry restoration
• Bulk viscosity of superfluid neutron stars
• Transport and hydrodynamics in the chiral limit
• Odd Parity Transport In Non-Abelian Superfluids From Symmetry Locking