Wigner-Smith time delay matrix for acoustic scattering: Theory and phenomenology

Utkarsh R Patel; Yiqian Mao; Eric Michielssen

doi:10.1121/10.0017826

Wigner-Smith time delay matrix for acoustic scattering: Theory and phenomenology

J Acoust Soc Am. 2023 May 1;153(5):2769. doi: 10.1121/10.0017826.

Authors

Utkarsh R Patel¹, Yiqian Mao¹, Eric Michielssen¹

Affiliation

¹ Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109-2122, USA.

PMID: 37133813
DOI: 10.1121/10.0017826

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.