  In the first part, we investigate the effect of long range particle exchange
in ideal bosonic chains. We establish that by using the Heisenberg formalism
along with matrix product state representation we can study the evolution as
well as the ground state of bosonic arrangements while including terms beyond
next-neighbour hopping. The method is then applied to analyse the quench
dynamics of condensates in a trapping potential and also to study the emergence
of entanglement as a result of collision in boson chains. In the second part,
we study the ground state as well as the dynamics of 1D boson arrangements with
local repulsive interactions and nearest-neighbour exchange using numerical
techniques based on time evolving block decimation (TEBD). We focus on the
development of quantum correlations between the terminal places of these
arrangements. We find that long-range entanglement in the ground state arises
as a result of intense boson tunnelling taking place across the whole chain in
systems with appropriate hopping coefficients. Additionally, we identify the
perturbations necessary to increase the entanglement between the end sites
above their ground state values. In the final part, we study the wave function
of a kicked condensate using a perturbative approach and compare the results
obtained in this way with numerical simulations.
