Hydrodynamic attractor and novel fixed points in superfluid Bjorken flow

Abstract

Extending the quantum effective approach of Son and Nicolis and incorporating dissipation, we develop a MIS formalism for describing a superfluid out of equilibrium by including the Goldstone boson and the condensate together with the hydrodynamic modes as the effective degrees of freedom. We find that the evolution of the superfluid undergoing Bjorken flow is governed by the conventional hydrodynamic attractor with unbroken symmetry and an even number of novel non-dissipative fixed points with broken symmetry. If the initial temperature is super-critical, then the condensate becomes exponentially small very rapidly and the system is trapped by the hydrodynamic attractor for a long intermediate time before it reheats rapidly and switches to one of the symmetry-breaking fixed points eventually. Finally, we show that the fixed points are unstable against inhomogeneous perturbations that should lead to spinodal decomposition. We conclude that these features should be generic beyond the MIS formalism.