  The out-of-equilibrium quantum dynamics of a Bose gas trapped in an
asymmetric double well and interacting with a finite-range interaction has been
studied in real space by solving the time-dependent many-body Schr\"odinger
equation numerically accurately using the multiconfigurational time-dependent
Hartree method for bosons (MCTDHB). We have focused on the weakly interacting
limit where the system is essentially condensed. We have examined the impact of
the range of the interaction on the dynamics of the system, both at the
mean-field and many-body levels. Explicitly, we have studied the maximal and
the minimal values of the many-body position variance in each cycle of
oscillation, and the overall pace of its growth. We find that the range of the
interaction affects the dynamics of the system differently for the right well
and the left well. We have also examined the infinite-particle limit and find
that even there, the impact of the range of the interaction can only be
described by a many-body theory such as MCTDHB.
