论文标题
部分可观测时空混沌系统的无模型预测
Chiral perturbative analysis for an almost massless neutrino in the type-I seesaw mechanism
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。
In this paper, we perform chiral perturbative analysis of an approximate lepton number symmetry associated with a sufficiently light neutrino in the type-I seesaw mechanism. For the Dirac mass matrix $m_{D} = (\bm A \, , \bm B \, , \bm C)$, linearly independent components of $\bm C$ from $\bm A$ and $\bm B$ are treated as symmetry-breaking parameters. A deviation in the eigenvector of the massless mode $δ\bm u$ occurs in the first-order perturbation and the lightest mass $m_{1 \, \rm or \, 3} \propto \det m_{D}^{2} / M_{3}$ emerges in the second-order. By solving the perturbation theory, we obtained specific expressions of $δ\bm u$ and $m_{1 \, \rm or \, 3}$. As a result, two complex parameters in $m_{D}$ are bounded to some extent from the eigenvector. These constraints are associated with the chiral symmetry and are not susceptible to renormalization.
