  Dynamical properties of two bosonic quantum walkers in a one-dimensional
lattice are studied theoretically. Depending on the initial state,
interactions, lattice tilting, and lattice disorder, whole plethora of
different behaviors are observed. Particularly, it is shown that two bosons
system manifests the many-body localization like behavior in the presence of a
quenched disorder. The whole analysis is based on a specific decomposition of
the temporal density profile into different contributions from singly and
doubly occupied sites. In this way, the role of interactions is extracted.
Since the contributions can be directly measured in experiments with ultra-cold
atoms in optical lattices, the predictions presented may have some importance
for upcoming experiment.
