  Exploring the impact of dimensionality on the quantum dynamics of interacting
bosons in traps including particle correlations is an interesting but
challenging task. Due to the different participating length scales the
modelling of the short-range interactions in three dimensions plays a special
role. We review different approaches for the latter and elaborate that for
multi-configurational computational strategies finite range potentials are
adequate resulting in the need of large grids to resolve the relevant length
scales. This results in computational challenges which include also the
exponential scaling of complexity with the number of atoms. We show that the
recently developed ab-initio Multi-Layer Multi-Configurational Time- Dependent
Hartee method for Bosons (ML-MCTDHB) [J. Chem. Phys. 139, 134103 (2013)] can
face both numerical challenges and present an efficient numerical
implementation of ML-MCTDHB in three spatial dimensions, particularly suited to
describe the quantum dynamics for elongated traps.
  The beneficial scaling of our approach is demonstrated by studying the
tunnelling dynamics of bosonic ensembles in a double well. Comparing
three-dimensional with quasi-one dimensional simulations, we find
dimensionality-induced effects in the density. Furthermore, we study the
crossover from weak transversal confinement, where a mean-field description of
the system is sufficient, towards tight transversal confinement, where particle
correlations and beyond mean-field effects are pronounced.
