论文标题
Wigner-Smith时间延迟矩阵用于声学散射：理论和现象学
Wigner-Smith Time Delay Matrix for Acoustic Scattering: Theory and Phenomenology
论文作者
论文摘要
Wigner-Smith（WS）时间延迟矩阵将无损系统的散射矩阵与其频率导数相关联。首先在量子力学领域提出，以表征粒子在碰撞期间经历的时间延迟，将WS时间延迟技术扩展到由Helmholtz方程控制的声学散射问题。得出了涉及能量密度的重新归一化体积积分的WS时间延迟矩阵的条目的表达，并显示出独立于散点子的几何形状，边界条件（声音柔软或声音）和激发的真实表达。数值示例表明，WS时间延迟矩阵的本征模描述了以明确定义的时间延迟为特征的独特散射现象。
The Wigner-Smith (WS) time delay matrix relates a lossless system's scattering matrix to its frequency derivative. First proposed in the realm of quantum mechanics to characterize time delays experienced by particles during a collision, this article extends the use of WS time delay techniques to acoustic scattering problems governed by the Helmholtz equation. Expression for the entries of the WS time delay matrix involving renormalized volume integrals of energy densities are derived, and shown to hold true independent of the scatterer's geometry, boundary condition (sound-soft or sound-hard), and excitation. Numerical examples show that the eigenmodes of the WS time delay matrix describe distinct scattering phenomena characterized by well-defined time delays.
