论文标题
与约旦块的电路进化矩阵的扰动
Perturbations of circuit evolution matrices with Jordan blocks
论文作者
论文摘要
在我们先前的研究中，我们合成具有涉及非平凡约旦块和相应退化特征频率的进化矩阵的特殊电路。这种类型的堕落有时被称为堕落的特殊点（EPD）。这些电路中最简单的电路仅由两个LC循环组成，与旋转器相连，在这里它们引起了我们的主要关注。这些简单的电路在附近EPD状态时可用于增强灵敏度应用。考虑到这一点，我们在这里为这些简单的电路提供了一个全面的扰动理论，并确保了它们稳定的操作。关于约旦区块的数值处理及其扰动的更广泛的问题，我们提出了一些方法，可以检测到与约旦块的接近度。
In our prior studies we synthesized special circuits possessing evolution matrices that involve nontrivial Jordan blocks and the corresponding degenerate eigenfrequencies. The degeneracy of this type is sometimes referred to as exceptional point of degeneracy (EPD). The simplest of these circuits are composed just of two LC-loops coupled by a gyrator and they are of our primary interest here. These simple circuits when near an EPD state can be used for enhanced sensitivity applications. With that in mind we develop here a comprehensive perturbation theory for these simple circuits near an EPD as well way to assure their stable operation. As to broader problem of numerical treatment of Jordan blocks and their perturbation we propose a few approaches allowing to detect the proximity to Jordan blocks.
