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.
翻译:Wigner-Smith(WS)时间延迟矩阵将一个无损系统散射矩阵与其频率衍生物相连接。首先,在量子力学领域提出了关于粒子在碰撞期间所经历的时间延误特征的建议,本条将WS时间延迟技术的使用扩大到由Helmholtz等式管辖的声学散射问题。WS时间延迟矩阵中含有能源密度重整体积积组成部分的条目的表达方式,并显示与散射器的几何、边界状况(声音软或声音硬性)和引力无关。数字性实例表明,WS时间延迟矩阵的偏差模型描述了以定义明确的时间延误为特征的明显散射现象。