Gubser流中的流体动力学吸引子和微扰展开的命运
Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
摘要：
微扰展开，如众所周知的梯度系列和最近提出的慢滚展开，最近已被用来调查的出现在系统中的流体动力学行为进行Bjorken流。在本文中，我们确定了第一次在Gubser流动的情况下，相对论流体力学中的这些微扰展开的高阶行为。虽然这两个系列发散，慢滚系列可以提供一个更好的整体描述系统的动态比梯度展开时，这两个系列都截断在低阶。截断的慢滚序列也可以描述Gubser流的吸引子解，只要系统足够接近原点附近的平衡（即，$ρ=0$）在$dS_3 \otimes \mathbb{R}$。与Bjorken流的情形不同，本文证明了Gubser流吸引子解不仅仅是有效Knudsen数$τ_R \sqrt{σ_{μν}σ^{μν}} \sim τ_R\, \tanhρ$的函数.我们的研究结果进一步支持的想法，新的\emph{resummed}本构关系之间的耗散电流和守恒量的梯度可以出现在系统远离平衡，超出了通常的梯度展开的有效性制度。
英文摘要：
Perturbative expansions, such as the well-known gradient series and the recently proposed slow-roll expansion, have been recently used to investigate the emergence of hydrodynamic behavior in systems undergoing Bjorken flow. In this paper we determine for the first time the large order behavior of these perturbative expansions in relativistic hydrodynamics in the case of Gubser flow. While both series diverge, the slow-roll series can provide a much better overall description of the system's dynamics than the gradient expansion when both series are truncated at low orders. The truncated slow-roll series can also describe the attractor solution of Gubser flow as long as the system is sufficiently close to equilibrium near the origin (i.e., $ρ=0$) in $dS_3 \otimes \mathbb{R}$. Differently than the case of Bjorken flow, here we show that the Gubser flow attractor solution is not solely a function of the effective Knudsen number $τ_R \sqrt{σ_{μν}σ^{μν}} \sim τ_R\, \tanhρ$. Our results give further support to the idea that new \emph{resummed} constitutiv relations between dissipative currents and the gradients of conserved quantities can emerge in systems far from equilibrium that are beyond the regime of validity of the usual gradient expansion.
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