  We investigate finite number effects in collisions between two states of an
initially well known number of identical bosons with contact interactions,
oscillating in the presence of harmonic confinement in one dimension. We
investigate two N/2 (interacting) ground states, which are initially displaced
from the trap center, and the effects of varying interaction strength. The
numerics focus on the simplest case of N=4. In the non-interacting case, such a
system would display periodic oscillation with a half harmonic oscillator
period (due to the left-right symmetry). With the addition contact interactions
between the bosons, collisions generate entanglement between each of the states
and distribute energy into other modes of the oscillator. We study the system
numerically via an exact diagonalization of the Hamiltonian with a finite
basis, investigating left/right number uncertainty as our primary measure of
entanglement. Additionally we study the time-evolution and equilibration of the
single-body von Neumann entropy for both the attractive and repulsive cases. We
identify parameter regimes for which attractive interactions create
qualitatively different behavior to repulsive interactions, due to the presence
of bound states (quantum solitons) and explain the processes behind this.
