论文标题
部分可观测时空混沌系统的无模型预测
Understanding thermal nature of de Sitter spacetime via inter-detector interaction
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。
The seminar discovery by Gibbons and Hawking that a freely falling detector observes an isotropic background of thermal radiation reveals that de Sitter space is equivalent to a thermal bath at the Gibbons-Hawking temperature in Minkowski space, as far as the response rate of the detector is concerned. Meanwhile, for a static detector which is endowed with a proper acceleration with respect to the local freely-falling detectors, the temperature becomes the square root of the sum of the squared Gibbons-Hawking temperature and the squared Unruh temperature associated with the proper acceleration of the detector. Here, we demonstrate, by examining the interaction of two static detectors in the de Sitter invariant vacuum, that de Sitter space in regard to its thermal nature is unique on its own right in the sense that it is even neither equivalent to the thermal bath in Minkowski space when the static detectors become freely-falling nor to the Unruh thermal bath at the cosmological horizon where the Unruh effect dominates, insofar as the behavior of the inter-detector interaction in de Sitter space dramatically differs both from that in the Minkowski thermal bath and the Unruh thermal bath.
