论文标题
富含对称性的拓扑阶段的G跨模块化
G-crossed Modularity of Symmetry-Enriched Topological Phases
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 universal properties of (2 + 1)D topological phases of matter enriched by a symmetry group G are described by G-crossed extensions of unitary modular tensor categories (UMTCs). While the fusion and braiding properties of quasiparticles associated with the topological order are described by a UMTC, the G-crossed extensions further capture the properties of the symmetry action, fractionalization, and defects arising from the interplay of the symmetry with the topological order. We describe the relation between the G-crossed UMTC and the topological state spaces on general surfaces that may include symmetry defect branch lines and boundaries that carry topological charge. We define operators in terms of the G-crossed UMTC data that represent the mapping class transformations for such states on a torus with one boundary, and show that these operators provide projective representations of the mapping class groups. This allows us to represent the mapping class group on general surfaces and ensures a consistent description of the corresponding symmetry-enriched topological phases on general surfaces. Our analysis also enables us to prove that a faithful G-crossed extension of a UMTC is necessarily G-crossed modular.
