Abstract

Based on algebraic methods, an exact solution is found to the inverse problem for a complex vibronic analogue of the Fermi resonance, which consists in determining from the spectral data for the observed conglomerate of lines (energies E_k and transition intensities I_k, k = 1, 2, …, n; n > 2) the energies of the dark states, A_m, and the matrix elements B_m of their coupling with the bright state. In the first part of the algorithm, using plane Jacobi rotations, an orthogonal similarity transformation matrix X is found, the first row of which is subject to the condition (X_1k)² = I_k on its elements, since only one unperturbed state is bright. In the second part, the quantities A_m and B_m are obtained from the solution of the eigenvalue problem for the block of dark states of the matrix Xdiag({E_k})X ^–1.

中文翻译：

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基于平面雅可比旋转的费米共振复振动模拟的反问题的求解

摘要

基于代数方法，找到了费米共振的复杂振动模拟的反问题的精确解，这包括根据观察到的线团（能量E _k和跃迁强度I _k，k = 1，2，…，n ; n > 2）暗态的能量A _m以及与亮态耦合的矩阵元素B _m。在算法的第一部分中，使用平面Jacobi旋转，找到正交相似度转换矩阵X，其第一行受条件（X _{1 k}）² = I _k在其元素上，因为只有一种不受干扰的状态是明亮的。在第二部分中，从矩阵X diag（{ E _k））X ^–1的暗态块的特征值问题的解中获得A _m和B _m。