论文标题

部分可观测时空混沌系统的无模型预测

Dynamical mean-field study of a photon-mediated ferroelectric phase transition

论文作者

Lenk, Katharina, Li, Jiajun, Werner, Philipp, Eckstein, Martin

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 interplay of light and matter gives rise to intriguing cooperative effects in quantum many-body systems. This is even true in thermal equilibrium, where the electromagnetic field can hybridize with collective modes of matter, and virtual photons can induce interactions in the solid. Here, we show how these light-mediated interactions can be treated using the dynamical mean-field theory formalism. We consider a minimal model of a two-dimensional material that couples to a surface plasmon polariton mode of a metal-dielectric interface. Within the mean-field approximation, the system exhibits a ferroelectric phase transition that is unaffected by the light-matter coupling. Bosonic dynamical mean-field theory provides a more accurate description and reveals that the photon-mediated interactions enhance the ferroelectric order and stabilize the ferroelectric phase.

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