Quantum Effects In Low Temperature Bosonic Systems

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.