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Extending the quantum effective approach of Son and Nicolis and incorporatingdissipation, we develop a MIS formalism for describing a superfluid out ofequilibrium by including the Goldstone boson and the condensate together withthe hydrodynamic modes as the effective degrees of freedom. We find that theevolution of the superfluid undergoing Bjorken flow is governed by theconventional hydrodynamic attractor with unbroken symmetry and an even numberof novel non-dissipative fixed points with broken symmetry. If the initialtemperature is super-critical, then the condensate becomes exponentially smallvery rapidly and the system is trapped by the hydrodynamic attractor for a longintermediate time before it reheats rapidly and switches to one of thesymmetry-breaking fixed points eventually. Finally, we show that the fixedpoints are unstable against inhomogeneous perturbations that should lead tospinodal decomposition. We conclude that these features should be genericbeyond the MIS formalism.

Hydrodynamic attractor and novel fixed points in superfluid Bjorken flow