Determine the character of the apparent precursor in the reduced response

Determine whether the apparent small noncausal component near t=0 in the numerically evaluated reduced Kerr response is genuinely noncausal, rather than a finite-frequency-resolution artifact.

Background

The supplemental analysis compares the exact reduced response with its causal rational approximation in the time domain. Near t=0, the exact numerical response displays a small apparent component at negative times that is absent from the rational approximation.

Because the Fourier integral is evaluated over a finite frequency range, the authors state that the plotted data do not suffice to resolve this component or rigorously establish whether it is genuinely noncausal. They further note that the reduced response is not the full retarded Green’s function and may therefore have different causal properties.