发表机构
GSI Helmholtzzentrum für Schwerionenforschung GmbH; Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität; Helmholtz Research Academy Hessen for FAIR (HFHF)（GSI亥姆霍兹重离子研究中心有限公司; 约翰·沃尔夫冈·歌德大学理论物理研究所; 黑森亥姆霍兹FAIR研究学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明小碰撞系统中各向异性流的差异源于不同角谐波弛豫速率，而非模型不确定性，并给出弛豫谱闭合解，揭示其与黏度等物理量的不同关联。
AI 中文摘要
当散射粒子气体受到扰动时，其速度分布的每个角谐波都以各自的速率衰减。流体力学及其中的剪切黏度仅依赖于这些速率中的一个，即四极谐波的速率。一个在停止相互作用前仅散射数次的气体会记住所有这些速率。这正是小碰撞系统（如 $p+p$、$p+$Pb 和 O$+$O）的情况，在这些系统中，调谐到相同黏度的动力学模型却预测出不同的各向异性流。我们表明，这种差异并非模型不确定性，而是对剩余速率的测量：在碰撞次数的一阶近似下，流响应的比值等于弛豫速率的比值，且与初始几何无关。对于 QCD 碰撞核，其中速率还依赖于动量，我们以闭合形式获得了弛豫模式的完整谱，并表明稀薄流、黏度和晚期衰变探测的是该谱的三种不同平均值。一个动量分辨的动力学求解器证实，角层级首先在软动量处丢失，且流响应稳定在单一速率模型无法产生的值上。同样的结构也支配着二维电子气和原子费米气体。
英文摘要
When a gas of scattering particles is disturbed, each angular harmonic of its velocity distribution decays at its own rate. Hydrodynamics, and with it the shear viscosity, depends on only one of these rates, the one for the quadrupole harmonic. A system that scatters only a few times before it stops interacting remembers all of them. This is the situation of small collision systems such as $p+p$, $p+$Pb and O$+$O, where kinetic models tuned to the same viscosity nevertheless predict different anisotropic flow. We show that this difference is not a model uncertainty but a measurement of the remaining rates: to first order in the number of collisions, ratios of flow responses equal ratios of relaxation rates, independently of the initial geometry. For the QCD collision kernel, where the rates also depend on momentum, we obtain the full spectrum of relaxation modes in closed form and show that dilute flow, viscosity, and late-time decay probe three different averages of it. A momentum-resolved kinetic solver confirms that the angular hierarchy is lost first at soft momenta and that the flow response settles at a value no single-rate model produces. The same structure governs two-dimensional electron and atomic Fermi gases.
Comments6 pages, 2 figures Supplemental material: 8 pages, 3 figures, 4 tables
