论文标题

部分可观测时空混沌系统的无模型预测

Symmetry Resolved Entanglement Entropy in Hyperbolic de Sitter Space

论文作者

Gaur, Himanshu, Yajnik, Urjit A.

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。

In this paper, we study the relation between entanglement and global internal symmetries on de Sitter space. We consider two symmetric causally disconnected regions in the hyperbolic chart on de Sitter space. Since entanglement measures characterises correlations, the study of entanglement between the two causally disconnected regions gives information about the long range correlations in de Sitter space. When a theory possesses an additive global internal symmetry, the entanglement measures for a state with fixed global charge may be decomposed into local charge sectors in either subsystem and thus providing a finer resolution of entanglement. Here we will consider two theories: free complex scalar field, and free Dirac field on de Sitter space. Both theories possess global internal $U(1)$ symmetry. We study the symmetry resolved entanglement entropy for both theories in the Bunch-Davies vacuum state. We find that the symmetry resolved entanglement entropy has equipartition into local charge sectors upto the terms that scale as $V_{H_3}^0$ in the limit of large $V_{H_3}$, where $V_{H_3}$ is the volume of either region. This equipartition however is only broken by the terms of order $O(1/V_{H_3})$. Consequently, we have equipartition of symmetry resolved entanglement entropy in the limit of infinite volume.

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