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We consider a model of electrons in a finite topological insulator. Wenumerically study the propagation of electronic wave-packets localized nearedges of the structure in the presence of defects and random disorder. Wecompare the propagation with computations of the \emph{spectral localizerindex}: a spatially local topological index. We find that without disorder,wave-packets propagate along boundaries between regions of differing spectrallocalizer index with minimal loss, even in the presence of strong defects. Withdisorder, wave-packets still propagate along boundaries between regions ofdiffering localizer index, but lose significant mass as they propagate. We alsofind that with disorder, the \emph{localizer gap}, a measure of the localizerindex "strength", is generally smaller away from the boundary than withoutdisorder. Based on this result, we conjecture that wave-packets propagatingalong boundaries between regions of differing spectral localizer index do notlose significant mass whenever the localizer gap is sufficiently large on bothsides of the boundary.

Wave-packet propagation in a finite topological insulator and the spectral localizer index