论文标题
耦合谐波振荡器系统中特征值从特征值恢复
Recovery of eigenvectors from eigenvalues in systems of coupled harmonic oscillators
论文作者
论文摘要
特征向量 - 元素值身份将Hermitian矩阵的特征向量与其特征值和其主要子膜的特征值联系起来，其中已删除了jth行和列的特征值。我们表明，由带有真实特征值的正方形矩阵描述的一维耦合谐振器提供了简单的物理系统，可以在实践中应用此公式。子系统由删除的jth谐振器组成，因此可以在物理上实现。仅凭光谱，就可以获得完整系统的振荡模式。连续的单谐振缺失原理在两个实验的耦合射频谐振阵列阵列的两个实验中得到了比最高的邻居耦合，其中使用网络分析仪测量了光谱。实验中涵盖了赫米尔米亚人和非弱者案例。在这两种情况下，如果考虑到系统对称性施加的某些一致性条件，则实验特征向量估计与数值模拟非常吻合。在Hermitian情况下，这些估计是仅从共振光谱中获得的，而无需了解系统参数。找到身体相关性仍然是一个有趣的问题，可以找到仅从光谱中获得完整的非官员特征向量集的条件。
The eigenvector-eigenvalue identity relates the eigenvectors of a Hermitian matrix to its eigenvalues and the eigenvalues of its principal submatrices in which the jth row and column have been removed. We show that one-dimensional arrays of coupled resonators, described by square matrices with real eigenvalues, provide simple physical systems where this formula can be applied in practice. The subsystems consist of arrays with the jth resonator removed, and thus can be realized physically. From their spectra alone, the oscillation modes of the full system can be obtained. This principle of successive single resonator deletions is demonstrated in two experiments of coupled radiofrequency resonator arrays with greater-than-nearest neighbor couplings, in which the spectra are measured with a network analyzer. Both the Hermitian as well as a non-Hermitian case are covered in the experiments. In both cases the experimental eigenvector estimates agree well with numerical simulations if certain consistency conditions imposed by system symmetries are taken into account. In the Hermitian case, these estimates are obtained from resonance spectra alone without knowledge of the system parameters. It remains an interesting problem of physical relevance to find conditions under which the full non-Hermitian eigenvector set can be obtained from the spectra alone.
