Understanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media has advanced the knowledge and applications of wave interactions. Here, we use analytic theory and numerical simulations to understand and control the transmission and transmission time in complex systems by deforming a medium and adjusting the level of gain or loss. Unlike the zeros of the scattering matrix, the position and motion of the zeros of the determinant of the transmission matrix (TM) in the complex plane of frequency and field decay rate have robust topological properties. In systems without loss or gain, the transmission zeros appear either singly on the real axis or as conjugate pairs in the complex plane. As the structure is modified, two single zeros and a complex conjugate pair of zeros may interconvert when they meet at a square root singularity in the rate of change of the distance between the transmission zeros in the complex plane with sample deformation. The transmission time is the spectral derivative of the argument of the determinant of the TM. It is a sum over Lorentzian functions associated with the resonances of the medium, which is the density of states, and with the zeros of the TM. Transmission vanishes, and the transmission time diverges as zeros are brought near the real axis. Monitoring the transmission and transmission time when two zeros are close may open new possibilities for ultrasensitive detection.

中文翻译：

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复杂系统中具有拓扑对称性的零传输

了解量子系统和超材料中的Fano共振中消失的传输以及无序介质中的完美和超低传输，已经提高了波相互作用的知识和应用。在这里，我们使用解析理论和数值模拟来了解和控制复杂系统中的传输和传输时间，方法是使介质变形并调整增益或损耗的水平。与散射矩阵的零点不同，传输矩阵（TM）的行列式的零点在频率和场衰减率的复平面中的位置和运动具有强大的拓扑特性。在没有损耗或增益的系统中，传输零点要么在实轴上单独出现，要么在复平面中作为共轭对出现。随着结构的修改，当两个单零点和一个复共轭零点在平方根奇异点相遇时，它们在复平面中透射零点之间的距离随样本变形的变化率会发生变化，它们可能会相互转换。传输时间是TM行列式自变量的频谱导数。它是洛伦兹函数的总和，该洛伦兹函数与介质的共振相关，该共振是状态的密度，并且与TM的零相关。传输消失，传输时间随着零接近实轴而发散。在两个零接近时监视传输和传输时间可能为超灵敏检测打开新的可能性。