论文标题
部分可观测时空混沌系统的无模型预测
On quasi-nodal spheres and the spin Hall effect: the case of YH3 and CaTe
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。
Band inversion is a known feature in a wide range of topological insulators characterized by a change of orbital type around a high-symmetry point close to the Fermi level. In some cases of band inversion in topological insulators, the existence of quasinodal spheres has been detected, and the change of orbital type is shown to be concentrated along these spheres in momentum space. To understand this phenomenon, we develop a local effective fourfold Hamiltonian that models the band inversion and reproduces the quasinodal sphere. This model shows that the signal of the spin Hall conductivity, as well as the change of orbital type, are both localized on the quasinodal sphere, and moreover, that these two indicators characterize the topological nature of the material. Using K-theoretical methods, we show that the change of orbital type parametrized by an odd clutching function is equivalent to the strong Fu-Kane-Mele invariant. We corroborate these results with ab initio calculations for the materials YH3 and CaTe, where in both cases the signal of the spin Hall conductivity is localized on the quasinodal spheres in momentum space. We conclude that a nontrivial spin Hall conductivity localized on the points of change of orbital type is a good indicator for topological insulation.
