Asymptotics of superfluid Bjorken flow

TL;DR

This paper analyzes the late-time behavior of an expanding superfluid modeled by a complex scalar field coupled to a viscous hydrodynamic theory, revealing novel asymptotic solutions with potential experimental implications.

Contribution

It introduces a new transseries solution form for superfluid Bjorken flow, capturing memory effects of symmetry breaking and different late-time behaviors based on condensate relaxation.

Findings

Asymptotic solutions involve a novel transseries with $ au^{-a ext{ln} au}$ factors.

Late-time behaviors include damped oscillations or pure damping depending on relaxation rate.

Oscillations may be observable in heavy ion collision experiments.

Abstract

We consider the dynamics of an expanding superfluid modeled by Mueller-Israel-Stewart theory coupled to a complex scalar field with a $U(1)$ symmetry that is spontaneously broken. This is a manageable theoretical setting for explorations of the chiral phase transition of expanding quark-gluon plasma. We study the late proper-time behavior of Bjorken flow in this physical system and find that asymptotic solutions can be expressed as a transseries of a novel form, which contains factors like $\tau^{-a\ln \tau}$. This transseries describes how the information encoded in the initial data is diluted in the course of dissipative evolution. These solutions retain memory of the symmetry-breaking transition and describe two qualitatively different late-time behaviors of the dynamical variables, depending on condensate relaxation rate: either a purely damped fall-off or damped oscillations. The possibility that such oscillations could be imprinted in the observed outcomes of heavy ion collision experiments is the main physical insight that follows from our analysis.