论文标题
总体框架及其吸引子中的保形比约肯流动：与穆勒 - 以色列 - 史特瓦特形式主义的相似之处和差异
Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism
论文作者
论文摘要
我们研究了一般框架方法对保形比约肯的含义，超出了早期的研究。我们表明，在后期的功率系列解决方案不是唯一的，并且伴随着$ 1/τ$的精确解决方案，如果在外壳上服用，该解决方案将变得毫无意义。与Müller-Israel-Stewart形式主义相反，$ \ nfsym $结果与水力扩展之间的匹配仅可能达到一阶，这会导致$η/s = 1/4π$。将结果与下一个顺序匹配会导致因果关系/稳定性值。此外，我们表明，通用框架中的压力各向异性无法捕获流体动物化，我们引入了一种替代度量来找到吸引者。使用慢速扩展，我们找到了吸引子的分析近似形式。我们还表明，吸引子的早期行为与稳定和因果关系有关。与稳定和因果关系相比，在稳定和因果状态之外的吸引者解决方案在早期引起了重新加热和负面的纵向压力。我们还评论了违反壳参数违反热力学的第二定律。我们表明，对于参数的稳定和因果选择，吸引子的外壳典型熵不是物理数量，在早期时期存在负差异，然后才趋于其壳上极限。另一方面，不稳定和可aus的吸引子具有非负熵差异。我们推测，对于一阶流体动力学的稳定性，需要违反第二定律和因果脱壳参数。我们研究了Borel转换系列的分析结构，并找到了杆子和非氢模式之间的适当关系。
We investigate the implications of the general frame approach for conformal Bjorken flow beyond the earlier studies. We show that the power series solution at late times is not unique and is accompanied by an exact solution of the form $1/τ$, which becomes unphysical if taken on shell. In contrast to the Müller-Israel-Stewart formalism, a matching between $\NFSYM$ results and the hydro expansion is only possible up to the first order, which gives rise to $η/s=1/4π$. Matching the results to the next order gives rise to causality/stability-violating values. Furthermore, we show that the pressure anisotropy in the general frame cannot capture the hydrodynamization, and we introduce an alternative measure to find the attractor. Using slow-roll expansion, we find an analytical approximation form for the attractor. We also show that the early-time behavior of attractors is related to stability and causality conditions. The attractor solutions outside the stable and causal regime give rise to reheating and negative longitudinal pressures in early times, in contrast to the stable and causal ones. We also comment on the violation of the second law of thermodynamics by the off-shell parameters. We show that for the stable and causal choice of parameters, the off-shell canonical entropy of the attractors, which is not a physical quantity, has a negative divergence in early times before tending to its on-shell limit. On the other hand, the unstable and acausal attractors have non-negative entropy divergence. We speculate that the violation of the second law by stable and causal off-shell parameters is required for stability of the first-order hydrodynamics. We investigate the analytical structure of the Borel-transformed series and find the proper relation between the poles and nonhydro modes.
