Wigner-Smith Time Delay Matrix for Acoustic Scattering: Theory and Phenomenology
Abstract
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.
Keywords
Cite
@article{arxiv.2205.07347,
title = {Wigner-Smith Time Delay Matrix for Acoustic Scattering: Theory and Phenomenology},
author = {Utkarsh R. Patel and Yiqian Mao and Eric Michielssen},
journal= {arXiv preprint arXiv:2205.07347},
year = {2023}
}
Comments
Submitted to The Journal of Acoustical Society of America