论文标题
部分可观测时空混沌系统的无模型预测
Time dependent field correlators from holographic EPR pairs
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。
We study the correlators of the fields that couple to the quark and anti-quark EPR pair in the super Yang-Mills theory using the holographic description, which is a string in AdS space with its two ends anchoring on the boundaries. We consider the cases that the endpoints of the string are static and that the endpoints are uniformly accelerated in opposite directions where the exact solutions for the string's profiles are available. In both cases, the two-point correlators of the boundary field, described by the linearized perturbations in the worldsheet, can also be derived exactly where we obtain the all-time evolution of the correlators. In the case of the accelerating string, the induced geometry on the string worldsheet has the causal structure of a two-sided AdS black hole with a wormhole connecting two causally disconnected boundaries, which can be a realization of the ER=EPR conjecture. We find that causality plays a crucial role in determining the nature of the dispersion relation of the particle and the feature of the induced mutual interaction between two particles from the field. In the case that two boundaries of the worldsheet are causally disconnected, the induced effect from the field gives the dissipative dynamics of each particle with no dependence on the distance between two particles, and the induced mutual coupling between them vanishes in the late times, following a power law. When two ends are causally connected, the induced dispersion relation becomes non-dissipative in the late times. Here, we will also comment on the implications of our findings to the entangled particle dynamics and the ER=EPR conjecture.
