  We study the dynamical properties of a few bosons confined in an
one-dimensional split hard wall trap with the interaction strength varying from
the weakly to strongly repulsive regime. The system is initially prepared in
one side of the double well by setting the barrier strength of the split trap
to be infinity and then the barrier strength is suddenly changed to a finite
value. Both exact diagonalization method and Bose-Hubbard model (BHM)
approximation are used to study the dynamical evolution of the initial system.
The exact results based on exact diagonaliztion verify the enhancement of
correlated tunneling in the strongly interacting regime. Comparing results
obtained by two different methods, we conclude that one-band BHM approximation
can well describe the dynamics in the weakly interacting regime, but is not
efficient to give quantitatively consistent results in the strongly interacting
regime. Despite of the quantitative discrepancy, we validate that the form of
correlated tunneling gives an important contribution to tunneling in the large
interaction regime. To get a quantitative description for the dynamics of
bosons in the strongly interacting regime, we find that a multi-band BHM
approximation is necessary.
