Heller Michal P, Jefferson Ro, Spaliński Michał, Svensson Viktor
Max Planck Institute for Gravitational Physics, Potsdam-Golm 14476, Germany.
National Centre for Nuclear Research, 02-093 Warsaw, Poland.
Phys Rev Lett. 2020 Sep 25;125(13):132301. doi: 10.1103/PhysRevLett.125.132301.
Hydrodynamic attractors have recently gained prominence in the context of early stages of ultrarelativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of view. In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions. We quantify this using principal component analysis. Furthermore, we adapt the well known slow-roll approximation to this setting. These techniques generalize easily to higher dimensional phase spaces, which we illustrate by a preliminary analysis of a dataset describing the evolution of a five-dimensional manifold of initial conditions immersed in a 16-dimensional representation of the phase space of the Boltzmann kinetic equation in the relaxation time approximation.
在相对论重离子对撞机（RHIC）和大型强子对撞机（LHC）的极端相对论性重离子碰撞早期阶段，流体动力学吸引子最近受到了广泛关注。我们从相空间的角度批判性地审视了关于这个主题的现有观点。在这种情况下，流体动力学吸引子可以被视为相空间区域动力学降维这一更普遍现象的一个特殊情况。我们使用主成分分析对此进行量化。此外，我们将著名的慢滚近似应用于这种情况。这些技术很容易推广到更高维的相空间，我们通过对一个数据集的初步分析来说明这一点，该数据集描述了在弛豫时间近似下，沉浸在玻尔兹曼动力学方程相空间的16维表示中的五维初始条件流形的演化。
