论文标题
部分可观测时空混沌系统的无模型预测
Chiral symmetry restoration at high matter density observed in pionic atoms
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Modern theories of physics tell that the vacuum is not an empty space. Hidden in the vacuum is a structure of anti-quarks $\bar{q}$ and quarks $q$. The $\bar{q}$ and $q$ pair has the same quantum number as the vacuum and condensates in it since the strong interaction of the quantum chromodynamics (QCD) is too strong to leave it empty. The $\bar{q}q$ condensation breaks the chiral symmetry of the vacuum. The expectation value $<\bar{q}q>$ is an order parameter. For higher temperature or higher matter-density, $|<\bar{q}q>|$ decreases reflecting the restoration of the symmetry. In contrast to these clear-cut arguments, experimental evidence is so far limited. First of all, the $\bar{q}q$ is nothing but the vacuum itself. It is neither visible nor perceptible. In this article, we unravel this invisible existence by high precision measurement of pionic atoms, $π^-$-meson-nucleus bound systems. Using the $π^-$ as a probe, we demonstrate that $|<\bar{q}q>|$ is reduced in the nucleus at 58% of the normal nuclear density by a factor of 77 $\pm$ 2% compared with that in the vacuum. This reduction indicates that the chiral symmetry is partially restored due to the extremely high density of the nucleus. The present experimental result clearly exhibits the existence of the hidden structure, the chiral condensate, in the vacuum.