Superfluids in expanding backgrounds and attractor times

TL;DR

This paper investigates the out-of-equilibrium behavior of superfluids with a Goldstone mode in expanding backgrounds, identifying attractor timescales and describing nonlinear evolution in cosmological and heavy ion collision contexts.

Contribution

It introduces the concept of attractor time in superfluid dynamics within expanding backgrounds and provides a comprehensive nonlinear evolution analysis, including novel regimes in Gubser flow.

Findings

Identification of a new attractor timescale dependent on initial conditions.

Complete nonlinear evolution description of superfluids in Gubser flow.

Observation of attractor behavior in superfluids in FLRW cosmological backgrounds.

Abstract

We determine the behavior of an out-of-equilibrium superfluid, composed of a $U(1)$ Goldstone mode coupled to hydrodynamic modes in a M\" uller-Israel-Stewart theory, in expanding backgrounds relevant to heavy ion collision experiments and cosmology. For suitable initial conditions, the evolution of the hydrodynamic variables leads to a change in the potential of the Goldstone mode, spontaneously breaking the symmetry. After some time, the condensate becomes small, leading the system evolution to be well described via hydrodynamic attractors for a timescale that we determine in Bjorken and Gubser flows. We define this new timescale as the \textit{attractor time} and show its dependence on initial conditions. In the case of the Gubser flow, we provide for the first time a complete description of the nonlinear evolution of the system, including a novel nonlinear regime of constant anisotropy not found in the Bjorken evolution. Finally, we consider the superfluid in the dynamical FLRW (Friedmann-Lemaitre-Roberston-Walker) background, where we observe a similar attractor behavior, dependent on the initial conditions, that at late times approaches a regime dominated by the condensate.