Time delays in anisotropic systems

TL;DR

This paper investigates how time delays in scattering processes differ between symmetric and asymmetric potentials, highlighting the unique properties of anisotropic systems and providing criteria to identify intrinsic symmetries.

Contribution

It clarifies the relationship between Wigner and Smith time delays in asymmetric potentials and introduces a criterion for recognizing potentials with hidden symmetries.

Findings

Wigner and Smith time delays coincide only for symmetric potentials.

Only one S-matrix formulation extends naturally to asymmetric potentials.

A criterion is provided to identify potentials with intrinsic symmetry.

Abstract

Scattering properties and time delays for general (non-symmetric) potentials in terms of the respective S-matrices are discussed paradigmatically in one dimension and in comparison to symmetric potentials. Only for the latter the Wigner and Smith time delays coincide. Considering asymmetric potentials also reveals that only one version of S-matrices used in the literature (the one with reflection coefficients on the diagonal) generalizes to the asymmetric case. Finally, we give a criterion how to identify a potential with intrinsic symmetry which behaves like an asymmetric one if it is merely offset from the scattering center.