The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics

Aniceto, Ines, Hasenbichler, Daniel and Olde Daalhuis, Adri (2023) The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics. Journal of Physics A: Mathematical and Theoretical, 56 (19), [195201]. (doi:10.1088/1751-8121/acc61d).

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Abstract

We use exponential asymptotics to match the late time temperature evolution of an expanding conformally invariant fluid to its early time behaviour. We show that the rich divergent transseries asymptotics at late times can be used to interpolate between the two regimes with exponential accuracy using the well-established methods of hyperasymptotics, Borel resummation and transasymptotics. This approach is generic and can be applied to any interpolation problem involving a local asymptotic transseries expansion as well as knowledge of the solution in a second region away from the expansion point. Moreover, we present global analytical properties of the solutions such as analytic approximations to the locations of the square-root branch points, exemplifying how the summed transseries contains within itself information about the observable in regions with different asymptotics.

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Accepted/In Press date: 21 March 2023

Published date: 19 April 2023

Additional Information: Funding Information: The authors would like to thank the participants of the focus week on Relativistic hydrodynamics during the programme Applicable Resurgent Asymptotics at the Isaac Newton Institute for the many relevant discussions that took place, and Ben Withers for his feedback on a draft of this work. The authors would also like to thank the Isaac Newton Institute for hosting them during the early stages of the work. IA has been supported by the UK EPSRC Early Career Fellowship EP/S004076/1, and the FCT-Portugal Grant PTDC/MAT-OUT/28784/2017. DH has been supported by the presidential scholarship of the University of Southampton. AOD’s research was supported by a research Grant 60NANB20D126 from the National Institute of Standards and Technology.

Keywords: bjorken flow, exponential asymptotics, relativistic hydrodynamics, resummation, transseries

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