Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
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Springer
Received: December Revised: April Accepted: June Published: July
11, 25, 25, 30,
2019 2020 2020 2020
Alireza Behtash,a Syo Kamata,a,b Mauricio Martineza and Haosheng Shia a
Department of Physics, North Carolina State University, Raleigh, NC 27695, U.S.A. b College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China
E-mail: [email protected], [email protected] , [email protected], [email protected] Abstract: In this work we introduce the generic conditions for the existence of a nonequilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models. Keywords: Heavy Ion Phenomenology, Phenomenological Models ArXiv ePrint: 1911.06406
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)226
JHEP07(2020)226
Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
Contents 1 Introduction and summary
1 5 6 7 10 19 21
3 Moment expansion method for the kinetic Gubser flow 3.1 Flow structure 3.1.1 Fixed point and stability 3.1.2 Global structure 3.2 Transseries construction 3.3 Stability analysis when N > 0, L > 0
24 27 27 30 31 34
4 Comparison with the Bjorken flow
35
5 Conclusions and final remarks
38
1
Introduction and summary
It is often argued in science and engineering textbooks that the regime of validity and applicability of hydrodynamics is linked to the existence of a hierarchy between the mean free path λm.f.p. and the system size L. The existence of such a hierarchy implies that the gradients of the fluid hydrodynamic fields are small compared to their corresponding thermal equilibrium configurations. In a modern approach, this also gives rise to the interpretation of hydrodynamics as an effective field theory for the slowly varying longwavelength modes of many-body systems in the form of a gradient expansion. This viewpoi
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