论文标题
部分可观测时空混沌系统的无模型预测
Unequal time Commutators in Friedmann universes: Deterministic evolution of massless fields
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 analyze minimally coupled massless scalar field in a Friedmann (FRW) universe in conformal co-ordinates to model the evolution of tensor perturbations and study the structure of the Wightman function therein. Using a duality map from a power law FRW universe to the de Sitter universe for such fields we obtain unequal time commutation relations between quantum field variables. We demonstrate that the commutation relations are invariant under state change and/or vacuum state selection. Using such commutators it is then possible to construct out of time ordered commutators (OTOC) in the FRW universes. The OTOCs are supposed to suggest the onset of chaotic behavior during the quantum evolution, we see that in case of Friedmann universes, unlike the scalar perturbations, the causal structure arrests the growth of quantum tensor perturbations for all the relevant epochs of the universe e.g. the de Sitter phase, the radiation dominated and the matter dominated era. Therefore the semi classical results of having a large backreaction and omnipresent noise in certain branches of the Friedmann universes with massless fields such as the tensor perturbations remain robust and stable.
