  We study the effects of long-range hopping and long-range inter-particle
interactions on quantum walk of hard-core bosons in ideal and disordered
one-dimensional lattices. We find that the range of hopping has a much more
significant effect on the particle correlation dynamics than the range of
interactions. We illustrate that long-range hopping makes the correlation
diagrams asymmetric with respect to the sign of the interaction and examine the
relative role of repulsive and attractive interactions on the dynamics of
scattering by isolated impurities and Anderson localization in dis- ordered
lattices. We show that weakly repulsive interactions increase the probability
of tunnelling through isolated impurities and decrease the localization.
